Relevant bibliographies by topics / Ordered Abelian groups

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Ordered Abelian groups'

Author: Grafiati
Published: 28 September 2024

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Journal articles on the topic "Ordered Abelian groups"

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Jakubík, Ján. "Retracts of abelian lattice ordered groups." Czechoslovak Mathematical Journal 39, no. 3 (1989): 477–85. http://dx.doi.org/10.21136/cmj.1989.102319.

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Glass, A. M. W. "Weakly abelian lattice-ordered groups." Proceedings of the American Mathematical Society 129, no. 3 (September 20, 2000): 677–84. http://dx.doi.org/10.1090/s0002-9939-00-05706-3.

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Conrad, Paul, and J. Roger Teller. "Abelian pseudo lattice ordered groups." Publicationes Mathematicae Debrecen 17, no. 1-4 (July 1, 2022): 223–41. http://dx.doi.org/10.5486/pmd.1970.17.1-4.26.

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Glass, A. M. W., Angus Macintyre, and Françoise Point. "Free abelian lattice-ordered groups." Annals of Pure and Applied Logic 134, no. 2-3 (July 2005): 265–83. http://dx.doi.org/10.1016/j.apal.2004.10.017.

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Glass, A. M. W. "Finitely presented ordered groups." Proceedings of the Edinburgh Mathematical Society 33, no. 2 (June 1990): 299–301. http://dx.doi.org/10.1017/s0013091500018204.

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Di Nola, Antonio, Giacomo Lenzi, Gaetano Vitale, and Roberto Giuntini. "Expanding Lattice Ordered Abelian Groups to Riesz Spaces." Mathematica Slovaca 72, no. 1 (February 1, 2022): 1–10. http://dx.doi.org/10.1515/ms-2022-0001.

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Abstract First we give a necessary and sufficient condition for an abelian lattice ordered group to admit an expansion to a Riesz space (or vector lattice). Then we construct a totally ordered abelian group with two non-isomorphic Riesz space structures, thus improving a previous paper where the example was a non-totally ordered lattice ordered abelian group. This answers a question raised by Conrad in 1975. We give also a partial solution to another problem considered in the same paper. Finally, we apply our results to MV-algebras and Riesz MV-algebras.
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GÖBEL, RÜDIGER, and SAHARON SHELAH. "CHARACTERIZING AUTOMORPHISM GROUPS OF ORDERED ABELIAN GROUPS." Bulletin of the London Mathematical Society 35, no. 03 (May 2003): 289–92. http://dx.doi.org/10.1112/s0024609302001881.

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Goffman. "COMPLETENESS IN TOTALLY ORDERED ABELIAN GROUPS." Real Analysis Exchange 20, no. 1 (1994): 58. http://dx.doi.org/10.2307/44152461.

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Dolich, Alfred, and John Goodrick. "Strong theories of ordered Abelian groups." Fundamenta Mathematicae 236, no. 3 (2017): 269–96. http://dx.doi.org/10.4064/fm256-5-2016.

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CLUCKERS, RAF, and IMMANUEL HALUPCZOK. "QUANTIFIER ELIMINATION IN ORDERED ABELIAN GROUPS." Confluentes Mathematici 03, no. 04 (December 2011): 587–615. http://dx.doi.org/10.1142/s1793744211000473.

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Dissertations / Theses on the topic "Ordered Abelian groups"

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McGuire, Alex Bernard. "Partially ordered Abelian groups and linearly compact domains." Thesis, University of Essex, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359787.

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Malekpour, Shirin Minoo. "Fuzzy predicate product logic and embeddings of ordered Abelian groups." College Park, Md. : University of Maryland, 2004. http://hdl.handle.net/1903/1697.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2004.
Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Russo, Anna Carla. "MV-algebras, Grothendieck toposes and applications." Doctoral thesis, Universita degli studi di Salerno, 2016. http://hdl.handle.net/10556/2308.

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2014 - 2015
This thesis is a contribution to the research program ‘toposes as bridges’ introduced in [12], which aims at developing the unifying potential of the notion of Grothendieck topos as a means for relating different mathematical theories to each other through topos-theoretic invariants. The general methodology outlined therein is applied here to study already existing categorical equivalences of particular interest arising in the field of many-valued logics and also to produce new ones. The original content of the disseration is contained in [22], [21] and [23]... [edited by Author]
XIV n.s.
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Hossain, Akash. "Forking in valued fields and related structures." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM019.

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Cette thèse est une contribution à la théorie des modèles des corps valués. On étudie la déviation dans les corps valués, ainsi que certains de leurs réduits. On s'intéresse particulièrement aux corps pseudo-locaux, les ultraproduits de caractéristique résiduelle nulle des corps valués p-adiques. Nous considérons d'abord aux groupes des valeurs des corps valués qui nous intéressent, les groupes Abéliens ordonnés réguliers. Nous y établissons description géométrique de la déviation, ainsi qu'une classification détaillée des extensions globales non-déviantes ou invariantes d'un type donné. Nous démontrons ensuite des principes d'Ax-Kochen-Ershov pour la division et la déviation dans la théorie resplendissante des expansions de suites exactes courtes pures de structures Abéliennes, telles qu'étudiées dans l'article sur la distalité d'Aschenbrenner-Chernikov-Gehret-Ziegler. En particulier, nos résultats s'appliquent aux groupes des termes dominants des (expansions de) corps valués. Pour finir, nous donnons diverses conditions suffisantes pour qu'un ensemble de paramètres soit une base d'extension dans un corps valué Hensélien de caractéristique résiduelle nulle. En particulier, nous démontrons que la déviation coïncide avec la division dans les corps pseudo-locaux de caractéristique résiduelle nulle. Nous discutons aussi des résultats de Ealy-Haskell-Simon sur la déviation pour les extensions séparées de corps valués Henséliens de caractéristique résiduelle nulle. Nous contribuons à la question en démontrant que, dans le cas d'une extension Abhyankar, et avec quelques hypothèses supplémentaires, la non-déviation d'un type dans in corps pseudo-local implique l'existence d'une mesure de Keisler globale invariante dont le support contient ce type, à l'instar des corps pseudo-finis
This thesis is a contribution to the model theory of valued fields. We study forking in valued fields and some of their reducts. We focus particularly on pseudo-local fields, the ultraproducts of residue characteristic zero of the p-adic valued fields. First, we look at the value groups of the valued fields we are interested in, the regular ordered Abelian groups. We establish for these ordered groups a geometric description of forking, as well as a full classification of the global extensions of a given type which are non-forking or invariant. Then, we prove an Ax-Kochen-Ershov principle for forking and dividing in expansions of pure short exact sequences of Abelian structures, as studied by Aschenbrenner-Chernikov-Gehret-Ziegler in their article about distality. This setting applies in particular to the leading-term structure of (expansions of) valued fields. Lastly, we give various sufficient conditions for a parameter set in a Henselian valued field of residue characteristic zero to be an extension base. In particular, we show that forking equals dividing in pseudo-local of residue characteristic zero. Additionally, we discuss results by Ealy-Haskell-Simon on forking in separated extensions of Henselian valued fields of residue characteristic zero. We contribute to the question in the setting of Abhyankar extensions, where we show that, with some additional conditions, if a type in a pseudo-local field does not fork, then there exists some global invariant Keisler measure whose support contains that type. This behavior is well-known in pseudo-finite fields
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Eyl, Jennifer S. "Spanning subsets of a finite abelian group of order pq /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/eylj/jennifereyl.pdf.

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Mut, Sagdicoglu Oznur. "On Finite Groups Admitting A Fixed Point Free Abelian Operator Group Whose Order Is A Product Of Three Primes." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610990/index.pdf.

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A long-standing conjecture states that if A is a finite group acting fixed point freely on a finite solvable group G of order coprime to jAj, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. If A is nilpotent, it is expected that the conjecture is true without the coprimeness condition. We prove that the conjecture without the coprimeness condition is true when A is a cyclic group whose order is a product of three primes which are coprime to 6 and the Sylow 2-subgroups of G are abelian. We also prove that the conjecture without the coprimeness condition is true when A is an abelian group whose order is a product of three primes which are coprime to 6 and jGj is odd.
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Flygare, Mattias. "Non-abelian braiding in abelian lattice models from lattice dislocations." Thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-31690.

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Topological order is a new field of research involving exotic physics. Among other things it has been suggested as a means for realising fault-tolerant quantum computation. Topological degeneracy, i.e. the ground state degeneracy of a topologically ordered state, is one of the quantities that have been used to characterize such states. Topological order has also been suggested as a possible quantum information storage. We study two-dimensional lattice models defined on a closed manifold, specifically on a torus, and find that these systems exhibit topological degeneracy proportional to the genus of the manifold on which they are defined. We also find that the addition of lattice dislocations increases the ground state degeneracy, a behaviour that can be interpreted as artificially increasing the genus of the manifold. We derive the fusion and braiding rules of the model, which are then used to calculate the braiding properties of the dislocations themselves. These turn out to resemble non-abelian anyons, a property that is important for the possibility to achieve universal quantum computation. One can also emulate lattice dislocations synthetically, by adding an external field. This makes them more realistic for potential experimental realisations.
Topologisk ordning är ett nytt område inom fysik som bland annat verkar lovande som verktyg för förverkligandet av kvantdatorer. En av storheterna som karakteriserar topologiska tillstånd är det totala antalet degenererade grundtillstånd, den topologiska degenerationen. Topologisk ordning har också föreslagits som ett möjligt sätt att lagra kvantdata. Vi undersöker tvådimensionella gittermodeller definierade på en sluten mångfald, specifikt en torus, och finner att dessa system påvisar topologisk degeneration som är proportionerlig mot mångfaldens topologiska genus. När dislokationer introduceras i gittret finner vi att grundtillståndets degeneration ökar, något som kan ses som en artificiell ökning av mångfaldens genus. Vi härleder sammanslagningsregler och flätningsregler för modellen och använder sedan dessa för att räkna ut flätegenskaperna hos själva dislokationerna. Dessa visar sig likna icke-abelska anyoner, en egenskap som är viktiga för möjligheten att kunna utföra universella kvantberäkningar. Det går också att emulera dislokationer i gittret genom att lägga på ett yttre fält. Detta gör dem mer realistiska för eventuella experimentella realisationer.
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Powell, Mark Andrew. "Second order algebraic knot concordance group." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5030.

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Let Knots be the abelian monoid of isotopy classes of knots S1 ⊂ S3 under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-Orr-Teichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . .The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice knots. The quotient C/F(1.5) contains all metabelian concordance obstructions. The Cochran-Orr-Teichner (1.5)-level two stage obstructions map the concordance class of a knot to a pointed set (COT (C/1.5),U). We define an abelian monoid of chain complexes P, with a monoid homomorphism Knots → P. We then define an algebraic concordance equivalence relation on P and therefore a group AC2 := P/ ~, our second order algebraic knot concordance group. The results of this thesis can be summarised in the following diagram: . That is, we define a group homomorphism C → AC2 which factors through C/F(1.5). We can extract the two stage Cochran-Orr-Teichner obstruction theory from AC2: the dotted arrows are morphisms of pointed sets. Our second order algebraic knot concordance group AC2 is a single stage obstruction group.
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Keil, Stefan. "On non-square order Tate-Shafarevich groups of non-simple abelian surfaces over the rationals." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/16901.

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Bei elliptischen Kurven E/K über einem Zahlkörper K zwingt die Cassels-Tate Paarung die Ordnung der Tate-Shafarevich Gruppe Sha(E/K) zu einem Quadrat. Ist A/K eine prinzipal polarisierte abelschen Varietät, so ist bewiesen, daß die Ordnung von Sha(A/K) ein Quadrat oder zweimal ein Quadrat ist. William Stein vermutet, daß es für jede quadratfreie positive ganze Zahl k eine abelsche Varietät A/Q gibt, mit #Sha(A/Q)=kn². Jedoch ist es ein offenes Problem was zu erwarten ist, wenn die Dimension von A/Q beschränkt wird. Betrachtet man ausschließlich abelsche Flächen B/Q, so liefern Resultate von Poonen, Stoll und Stein Beispiele mit #Sha(B/Q)=kn², für k aus {1,2,3}. Diese Arbeit studiert tiefgehend nicht-einfache abelsche Flächen B/Q, d.h. es gibt elliptische Kurven E_1/Q und E_2/Q und eine Isogenie phi: E_1 x E_2 -> B. Relativ zur quadratischen Ordnung der Tate-Shafarevich Gruppe von E_1 x E_2 soll die Ordnung von Sha(B/Q) bestimmt werden. Um dieses Ziel zu erreichen wird die Isogenie-Invarianz der Vermutung von Birch und Swinnerton-Dyer ausgenutzt. Für jedes k aus {1,2,3,5,6,7,10,13,14} wird eine nicht-einfache, nicht-prinzipal polarisierte abelsche Fläche B/Q konstruiert, mit #Sha(B/Q)=kn². Desweiteren wird computergestützt berechnet wie oft #Sha(B/Q)=5n², sofern die Isogenie phi: E_1 x E_2 -> B zyklisch vom Grad 5 ist. Es stellt sich heraus, daß dies bei circa 50% der ersten 20 Millionen Beispielen der Fall ist. Abschließend wird gezeigt, daß wenn phi: E_1 x E_2 -> B zyklisch ist und #Sha(B/Q)=kn², so liegt k in {1,2,3,5,6,7,10,13}. Bei allgemeinen Isogenien phi: E_1 x E_2 -> B bleibt es unklar, ob k nur endlich viele verschiedene Werte annehmen kann. Im Anhang wird auf abelsche Flächen eingegangen, welche isogen zu der Jacobischen J einer hyperelliptischen Kurve über Q sind. Mit den in dieser Arbeit entwickelten Techniken können, anhand gewisser zyklischer Isogenien phi: J -> B, für jedes k in {11,17,23,29} Beispiele mit #Sha(B/Q)=kn² gegeben werden.
For elliptic curves E/K over a number field K the Cassels-Tate pairing forces the order of the Tate-Shafarevich group Sha(E/K) to be a perfect square. It is known, that if A/K is a principally polarised abelian variety, then the order of Sha(A/K) is a square or twice a square. William Stein conjectures that for any given square-free positive integer k there is an abelian variety A/Q, such that #Sha(A/Q)=kn². However, it is an open question what to expect if the dimension of A/Q is bounded. Restricting to abelian surfaces B/Q, then results of Poonen, Stoll and Stein imply that there are examples such that #Sha(B/Q)=kn², for k in {1,2,3}. In this thesis we focus in depth on non-simple abelian surfaces B/Q, i.e. there are elliptic curves E_1/Q and E_2/Q and an isogeny phi: E_1 x E_2 -> B. We want to compute the order of Sha(B/Q) with respect to the order of the Tate-Shafarevich group of E_1 x E_2, which has square order. To achieve this goal, we explore the invariance under isogeny of the Birch and Swinnerton-Dyer conjecture. For each k in {1,2,3,5,6,7,10,13,14} we construct a non-simple non-principally polarised abelian surface B/Q, such that #Sha(B/Q)=kn². Furthermore, we compute numerically how often the order of Sha(B/Q) equals five times a square, for cyclic isogenies phi: E_1 x E_2 -> B of degree 5. It turns out that this happens to be the case in approx. 50% of the first 20 million examples we have checked. Finally, we prove that if there is a cyclic isogeny phi: E_1 x E_2 -> B and #Sha(B/Q)=kn², then k is in {1,2,3,5,6,7,10,13}. For general isogenies phi: E_1 x E_2 -> B it remains unclear, whether there are only finitely many possibilities for k. In the appendix, we briefly consider abelian surfaces B/Q being isogenous to Jacobians J of hyperelliptic curves over Q. The techniques developed in this thesis allow to understand certain cyclic isogenies phi: J -> B. For each k in {11,17,23,29}, we provide an example with #Sha(B/Q)=kn².
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Ugarte, Guerra Francisco. "Valoraciones y relaciones de dominaci´on en grupos abelianos sin torsión." Pontificia Universidad Católica del Perú, 2016. http://repositorio.pucp.edu.pe/index/handle/123456789/96858.

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We define valuations and dominance relations in torsion-free abelian groups and prove that they are essentially the same objects. Next we show that valuations correspond with ltrations of subgroups closed under division by integers. We also prove that every torsion-free abelian valued group can be embedded in the Hahn product of subgroups defined by the respective valuations.
En este trabajo definimos valoraciones y relaciones de dominación en grupos abelianos sin torsión y probamos que estos son esencialmente los mismos objetos. Adicionalmente probamos que las valoraciones también se corresponden con filtraciones de subgrupos cerrados por división por enteros y que todo grupo abeliano valorado y sin torsión puede sumergirse en el producto de Hahn de subgrupos definidos por la valoración.
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Books on the topic "Ordered Abelian groups"

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Arnold, David M. Abelian Groups and Representations of Finite Partially Ordered Sets. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8750-1.

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Partially ordered abelian groups with interpolation. Providence, R.I: American Mathematical Society, 1986.

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Goodearl, K. R. Partially Ordered Abelian Groups with Interpolation. American Mathematical Society, 2010.

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Lenski, Wolfgang Wilhelm. Ordered Abelian groups in logics with Ramsey quantifiers. 1988.

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Arnold, David. Abelian Groups and Representations of Finite Partially Ordered Sets. Springer, 2012.

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Arnold, David. Abelian Groups and Representations of Finite Partially Ordered Sets. Springer London, Limited, 2012.

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Arnold, David. Abelian Groups and Representations of Finite Partially Ordered Sets (CMS Books in Mathematics). Springer, 2000.

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Caramello, Olivia. Examples of theories of presheaf type. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0011.

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This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.
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Book chapters on the topic "Ordered Abelian groups"

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Efrat, Ido. "Ordered Abelian groups." In Mathematical Surveys and Monographs, 15–35. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/124/02.

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Weispfenning, Volker. "Model Theory of Abelian l-Groups." In Lattice-Ordered Groups, 41–79. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2283-9_4.

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Darnel, Michael R. "Representable and Abelian Ω-groups." In Theory of Lattice-Ordered Groups, 301–58. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003067337-9.

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Arnold, David M. "Torsion-Free Abelian Groups." In Abelian Groups and Representations of Finite Partially Ordered Sets, 47–75. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8750-1_2.

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Mundici, Daniele. "Computing on Lattice-Ordered Abelian Groups." In Fields of Logic and Computation III, 210–25. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48006-6_15.

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Glass, A. M. W., and Françoise Point. "Finitely Presented Abelian Lattice-Ordered Groups." In Lecture Notes in Computer Science, 160–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75939-3_11.

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Melnikov, Alexander G. "Computable Ordered Abelian Groups and Fields." In Programs, Proofs, Processes, 321–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13962-8_36.

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Marra, Vincenzo, and Daniele Mundici. "MV-Algebras and Abelian l-Groups: a Fruitful Interaction." In Ordered Algebraic Structures, 57–88. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3627-4_4.

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Arnold, David M. "Butler Groups." In Abelian Groups and Representations of Finite Partially Ordered Sets, 76–125. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4419-8750-1_3.

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Lucas, F. "Some Applications of Definable Spine Analysis in Ordered Abelian Groups." In Ordered Algebraic Structures, 123–28. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2472-7_10.

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Conference papers on the topic "Ordered Abelian groups"

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Cavallo, Bice, Livia D'Apuzzo, and Massimo Squillante. "A SURVEY ON PAIRWISE COMPARISON MATRICES OVER ABELIAN LINEARLY ORDERED GROUPS." In The International Symposium on the Analytic Hierarchy Process. Creative Decisions Foundation, 2011. http://dx.doi.org/10.13033/isahp.y2011.093.

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Preeti, Agin Kumari, Amit Sehgal, Sarita Sehgal, Yashpal, and Sunil Kumar. "Counting subgroup series of abelian p-group which contains a subgroup of order p." In ADVANCES IN BASIC SCIENCE (ICABS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5122623.

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