Relevant bibliographies by topics / Noncommutative rings

Academic literature on the topic 'Noncommutative rings'

Author: Grafiati
Published: 4 June 2021
Last updated: 27 January 2023

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Contents

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

Journal articles on the topic "Noncommutative rings":

1

Buckley, S., and D. MacHale. "Noncommutative Anticommutative Rings." Irish Mathematical Society Bulletin 0018 (1987): 55–57. http://dx.doi.org/10.33232/bims.0018.55.57.

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Cohn, P. M. "NONCOMMUTATIVE NOETHERIAN RINGS." Bulletin of the London Mathematical Society 20, no. 6 (November 1988): 627–29. http://dx.doi.org/10.1112/blms/20.6.627.

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KAUCIKAS, ALGIRDAS, and ROBERT WISBAUER. "NONCOMMUTATIVE HILBERT RINGS." Journal of Algebra and Its Applications 03, no. 04 (December 2004): 437–43. http://dx.doi.org/10.1142/s0219498804000964.

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Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. This notion was extended to noncommutative rings in two different ways by the requirement that prime ideals are the intersection of maximal or of maximal left ideals, respectively. Here we propose to define noncommutative Hilbert rings by the property that strongly prime ideals are the intersection of maximal ideals. Unlike for the other definitions, these rings can be characterized by a contraction property: R is a Hilbert ring if and only if for all n∈ℕ every maximal ideal [Formula: see text] contracts to a maximal ideal of R. This definition is also equivalent to [Formula: see text] being finitely generated as an [Formula: see text]-module, i.e., a liberal extension. This gives a natural form of a noncommutative Hilbert's Nullstellensatz. The class of Hilbert rings is closed under finite polynomial extensions and under integral extensions.
4

Alajbegovic̀, Jusuf H., and Nikolai I. Dubrovin. "Noncommutative prüfer rings." Journal of Algebra 135, no. 1 (November 1990): 165–76. http://dx.doi.org/10.1016/0021-8693(90)90155-h.

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Dubrovin, N. I. "NONCOMMUTATIVE PRÜFER RINGS." Mathematics of the USSR-Sbornik 74, no. 1 (February 28, 1993): 1–8. http://dx.doi.org/10.1070/sm1993v074n01abeh003330.

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Wang, Jian, Yunxia Li, and Jiangsheng Hu. "Noncommutative G-semihereditary rings." Journal of Algebra and Its Applications 17, no. 01 (January 2018): 1850014. http://dx.doi.org/10.1142/s0219498818500147.

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In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [Formula: see text] is a commutative ring. Some new characterizations of left [Formula: see text]-semihereditary rings are given. Applications go in three directions. The first is to give a sufficient condition when a finitely presented right [Formula: see text]-module is Gorenstein flat if and only if it is Gorenstein projective provided that [Formula: see text] is left coherent. The second is to investigate the relationships between Gorenstein flat modules and direct limits of finitely presented Gorenstein projective modules. The third is to obtain some new characterizations of semihereditary rings, [Formula: see text]-[Formula: see text] rings and [Formula: see text] rings.
7

Ghorbani, A., and M. Naji Esfahani. "On noncommutative FGC rings." Journal of Algebra and Its Applications 14, no. 07 (April 24, 2015): 1550109. http://dx.doi.org/10.1142/s0219498815501091.

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Many studies have been conducted to characterize commutative rings whose finitely generated modules are direct sums of cyclic modules (called FGC rings), however, the characterization of noncommutative FGC rings is still an open problem, even for duo rings. We study FGC rings in some special cases, it is shown that a local Noetherian ring R is FGC if and only if R is a principal ideal ring if and only if R is a uniserial ring, and if these assertions hold R is a duo ring. We characterize Noetherian duo FGC rings. In fact, it is shown that a duo ring R is a Noetherian left FGC ring if and only if R is a Noetherian right FGC ring, if and only if R is a principal ideal ring.
8

Zabavskii, B. V. "Noncommutative elementary divisor rings." Ukrainian Mathematical Journal 39, no. 4 (1988): 349–53. http://dx.doi.org/10.1007/bf01060766.

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Gatalevich, A. I., and B. V. Zabavs'kii. "Noncommutative elementary divisor rings." Journal of Mathematical Sciences 96, no. 2 (August 1999): 3013–16. http://dx.doi.org/10.1007/bf02169697.

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MacKenzie, Kenneth W. "Polycyclic group rings and unique factorisation rings." Glasgow Mathematical Journal 36, no. 2 (May 1994): 135–44. http://dx.doi.org/10.1017/s0017089500030676.

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Abstract:
The theory of unique factorisation in commutative rings has recently been extended to noncommutative Noetherian rings in several ways. Recall that an element x of a ring R is said to be normalif xR = Rx. We will say that an element p of a ring R is (completely) prime if p is a nonzero normal element of R and pR is a (completely) prime ideal. In [2], a Noetherian unique factorisation domain (or Noetherian UFD) is defined to be a Noetherian domain in which every nonzero prime ideal contains a completely prime element: this concept is generalised in [4], where a Noetherian unique factorisation ring(or Noetherian UFR) is defined as a prime Noetherian ring in which every nonzero prime ideal contains a nonzero prime element; note that it follows from the noncommutative version of the Principal Ideal Theorem that in a Noetherian UFR, if pis a prime element then the height of the prime ideal pR must be equal to 1. Surprisingly many classes of noncommutative Noetherian rings are known to be UFDs or UFRs: see [2] and [4] for details. This theory has recently been extended still further, to cover certain classes of non-Noetherian rings: see [3].
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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Noncommutative rings":

1

Zhang, Yufei. "Orderings on noncommutative rings." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0013/NQ32804.pdf.

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Pandian, Ravi Samuel. "The structure of semisimple Artinian rings." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/2977.

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Proves two famous theorems attributed to J.H.M. Wedderburn, which concern the structure of noncommutative rings. The two theorems include, (1) how any semisimple Artinian ring is the direct sum of a finite number of simple rings; and, (2) the Wedderburn-Artin Theorem. Proofs in this paper follow those outlined in I.N. Herstein's monograph Noncommutative Rings with examples and details provided by the author.
3

Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.

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Nordstrom, Hans Erik. "Associated primes over Ore extensions and generalized Weyl algebras /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3181118.

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Thesis (Ph. D.)--University of Oregon, 2005.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 48-49). Also available for download via the World Wide Web; free to University of Oregon users.
5

Leroux, Christine M. "On universal localization of noncommutative Noetherian rings." Thesis, Northern Illinois University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3567765.

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The concepts of middle annihilators and links between prime ideals have been useful in studying classical localization. Universal localization has given us an alternative to classical localization as an approach to studying the localization of noncommutative Noetherian rings at prime and semiprime ideals. There are two main ideas we explore in this thesis. The first idea is the relationship between certain middle annihilator ideals, links between prime ideals, and universal localization. The second idea is to explore the circumstances under which the universal localization of a ring will be Noetherian, in the case where the ring is finitely generated as a module over its center.

6

Collier, Nicholas Richard. "On asymptotic stability of prime ideals in noncommutative rings." Thesis, University of Warwick, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403145.

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Brandl, Mary-Katherine. "Primitive and Poisson spectra of non-semisimple twists of polynomial algebras /." view abstract or download file of text, 2001. http://wwwlib.umi.com/cr/uoregon/fullcit?p3024507.

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Thesis (Ph. D.)--University of Oregon, 2001.
Typescript. Includes vita and abstract. Includes bibliographical references (leaf 49). Also available for download via the World Wide Web; free to University of Oregon users.
8

Low, Gordan MacLaren. "Injective modules and representational repleteness." Thesis, University of Glasgow, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319776.

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Rogozinnikov, Evgenii [Verfasser], and Anna [Akademischer Betreuer] Wienhard. "Symplectic groups over noncommutative rings and maximal representations / Evgenii Rogozinnikov ; Betreuer: Anna Wienhard." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1215758219/34.

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Brazfield, Christopher Jude. "Artin-Schelter regular algebras of global dimension 4 with two degree one generators /." view abstract or download file of text, 1999. http://wwwlib.umi.com/cr/uoregon/fullcit?p9947969.

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Abstract:
Thesis (Ph. D.)--University of Oregon, 1999.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 103-105). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9947969.
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Books on the topic "Noncommutative rings":

1

Montgomery, Susan, and Lance Small, eds. Noncommutative Rings. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4613-9736-6.

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2

McConnell, J. C. Noncommutative Noetherian rings. Chichester: Wiley, 1987.

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3

McConnell, J. C. Noncommutative Noetherian rings. Providence, R.I: American Mathematical Society, 2001.

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4

McConnell, J. C. Noncommutative Noetherian rings. Chichester [West Sussex]: Wiley, 1988.

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5

Lam, T. Y. A first course in noncommutative rings. 2nd ed. New York: Springer, 2001.

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6

Goodearl, K. R. An introduction to noncommutative Noetherian rings. Cambridge [England]: Cambridge University Press, 1989.

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Goodearl, K. R. An introduction to noncommutative Noetherian rings. 2nd ed. Cambridge, U.K: Cambridge University Press, 2004.

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Goodearl, K. R. An introduction to noncommutative noetherian rings. 2nd ed. Cambridge, U.K: Cambridge Univeristy Press, 2004.

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9

Dougherty, Steven, Alberto Facchini, André Leroy, Edmund Puczyłowski, and Patrick Solé, eds. Noncommutative Rings and Their Applications. Providence, Rhode Island: American Mathematical Society, 2015. http://dx.doi.org/10.1090/conm/634.

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10

Connes, Alain. Noncommutative geometry. San Diego: Academic Press, 1994.

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Book chapters on the topic "Noncommutative rings":

1

Shafarevich, Igor R. "Noncommutative Rings." In Encyclopaedia of Mathematical Sciences, 61–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26474-4_8.

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Bokhut’, L. A., I. V. L’vov, and V. K. Kharchenko. "Noncommutative Rings." In Encyclopaedia of Mathematical Sciences, 1–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-72899-0_1.

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Brungs, H. H. "Noncommutative Valuation Rings." In Perspectives in Ring Theory, 105–15. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2985-2_10.

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Warfield, R. B. "Noncommutative localized rings." In Lecture Notes in Mathematics, 178–200. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0099512.

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Knapp, Anthony W. "Modules over Noncommutative Rings." In Basic Algebra, 553–91. Boston, MA: Birkhäuser Boston, 2006. http://dx.doi.org/10.1007/978-0-8176-4529-8_10.

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Shafarevich, Igor R. "Modules over Noncommutative Rings." In Encyclopaedia of Mathematical Sciences, 74–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26474-4_9.

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Keeler, Dennis S. "The Rings of Noncommutative Projective Geometry." In Advances in Algebra and Geometry, 195–207. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-12-5_17.

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Akalan, Evrim, and Hidetoshi Marubayashi. "Multiplicative Ideal Theory in Noncommutative Rings." In Springer Proceedings in Mathematics & Statistics, 1–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-38855-7_1.

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Facchini, Alberto. "Commutative Monoids, Noncommutative Rings and Modules." In New Perspectives in Algebra, Topology and Categories, 67–111. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-84319-9_3.

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Ganchev, Alexander. "Fusion Rings and Tensor Categories." In Noncommutative Structures in Mathematics and Physics, 295–98. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0836-5_23.

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Conference papers on the topic "Noncommutative rings":

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MORI, IZURU. "NONCOMMUTATIVE PROJECTIVE SCHEMES AND POINT SCHEMES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0014.

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Bergamaschi, Flaulles Boone, and Regivan H. N. Santiago. "Strongly prime fuzzy ideals over noncommutative rings." In 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2013. http://dx.doi.org/10.1109/fuzz-ieee.2013.6622346.

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Elhassani, Mustapha, Aziz Boulbot, Abdelhakim Chillali, and Ali Mouhib. "Fully homomorphic encryption scheme on a nonCommutative ring R." In 2019 International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS). IEEE, 2019. http://dx.doi.org/10.1109/isacs48493.2019.9068892.

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