Log in

Relevant bibliographies by topics / Leavitt path algebras over arbitrary rings / Journal articles

Journal articles on the topic 'Leavitt path algebras over arbitrary rings'

To see the other types of publications on this topic, follow the link: Leavitt path algebras over arbitrary rings.

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 18 journal articles for your research on the topic 'Leavitt path algebras over arbitrary rings.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Nordstrom, Hans, and Jennifer A. Firkins Nordstrom. "Leavitt path algebras over arbitrary unital rings and algebras." Journal of Algebra and Its Applications 19, no. 06 (May 31, 2019): 2050107. http://dx.doi.org/10.1142/s0219498820501078.

Full text

Abstract:

We expand the work of Tomforde by further extending the construction of Leavitt path algebras (LPAs) over arbitrary associative, unital rings. We show that many of the results over a commutative ring hold in the more general setting, provide some useful generalizations of prior results, and give a definition for an iterated Leavitt path extension in our context.

APA, Harvard, Vancouver, ISO, and other styles

2

Nystedt, Patrik, and Johan Öinert. "Group gradations on Leavitt path algebras." Journal of Algebra and Its Applications 19, no. 09 (August 20, 2019): 2050165. http://dx.doi.org/10.1142/s0219498820501650.

Full text

Abstract:

Given a directed graph [Formula: see text] and an associative unital ring [Formula: see text] one may define the Leavitt path algebra with coefficients in [Formula: see text], denoted by [Formula: see text]. For an arbitrary group [Formula: see text], [Formula: see text] can be viewed as a [Formula: see text]-graded ring. In this paper, we show that [Formula: see text] is always nearly epsilon-strongly [Formula: see text]-graded. We also show that if [Formula: see text] is finite, then [Formula: see text] is epsilon-strongly [Formula: see text]-graded. We present a new proof of Hazrat’s characterization of strongly [Formula: see text]-graded Leavitt path algebras, when [Formula: see text] is finite. Moreover, if [Formula: see text] is row-finite and has no source, then we show that [Formula: see text] is strongly [Formula: see text]-graded if and only if [Formula: see text] has no sink. We also use a result concerning Frobenius epsilon-strongly [Formula: see text]-graded rings, where [Formula: see text] is finite, to obtain criteria which ensure that [Formula: see text] is Frobenius over its identity component.

APA, Harvard, Vancouver, ISO, and other styles

3

Rigby, Simon W., and Thibaud van den Hove. "A classification of ideals in Steinberg and Leavitt path algebras over arbitrary rings." Journal of Algebra 588 (December 2021): 200–249. http://dx.doi.org/10.1016/j.jalgebra.2021.08.021.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

STEINBERG, BENJAMIN. "CHAIN CONDITIONS ON ÉTALE GROUPOID ALGEBRAS WITH APPLICATIONS TO LEAVITT PATH ALGEBRAS AND INVERSE SEMIGROUP ALGEBRAS." Journal of the Australian Mathematical Society 104, no. 3 (March 28, 2018): 403–11. http://dx.doi.org/10.1017/s1446788717000374.

Full text

Abstract:

The author has previously associated to each commutative ring with unit$R$and étale groupoid$\mathscr{G}$with locally compact, Hausdorff and totally disconnected unit space an$R$-algebra$R\,\mathscr{G}$. In this paper we characterize when$R\,\mathscr{G}$is Noetherian and when it is Artinian. As corollaries, we extend the characterization of Abrams, Aranda Pino and Siles Molina of finite-dimensional and of Noetherian Leavitt path algebras over a field to arbitrary commutative coefficient rings and we recover the characterization of Okniński of Noetherian inverse semigroup algebras and of Zelmanov of Artinian inverse semigroup algebras.

APA, Harvard, Vancouver, ISO, and other styles

5

Özdin, Tufan. "On endomorphism rings of Leavitt path algebras." Filomat 32, no. 4 (2018): 1175–81. http://dx.doi.org/10.2298/fil1804175o.

Full text

Abstract:

Let E be an arbitrary graph, K be any field and A be the endomorphism ring of L := LK(E) considered as a right L-module. Among the other results, we prove that: (1) if A is a von Neumann regular ring, then A is dependent if and only if for any two paths in L satisfying some conditions are initial of each other, (2) if A is dependent then LK(E) is morphic, (3) L is morphic and von Neumann regular if and only if L is semisimple and every homogeneous component is artinian.

APA, Harvard, Vancouver, ISO, and other styles

6

ABRAMS, GENE, JASON P. BELL, PINAR COLAK, and KULUMANI M. RANGASWAMY. "TWO-SIDED CHAIN CONDITIONS IN LEAVITT PATH ALGEBRAS OVER ARBITRARY GRAPHS." Journal of Algebra and Its Applications 11, no. 03 (May 24, 2012): 1250044. http://dx.doi.org/10.1142/s0219498811005713.

Full text

Abstract:

Let E be any directed graph, and K be any field. For any ideal I of the Leavitt path algebra LK(E) we provide an explicit description of a set of generators for I. This description allows us to classify the two-sided noetherian Leavitt path algebras over arbitrary graphs. This extends similar results previously known only in the row-finite case. We provide a number of additional consequences of this description, including an identification of those Leavitt path algebras for which all two-sided ideals are graded. Finally, we classify the two-sided artinian Leavitt path algebras over arbitrary graphs.

APA, Harvard, Vancouver, ISO, and other styles

7

VAŠ, LIA. "GRADED CHAIN CONDITIONS AND LEAVITT PATH ALGEBRAS OF NO-EXIT GRAPHS." Journal of the Australian Mathematical Society 105, no. 2 (December 12, 2017): 229–56. http://dx.doi.org/10.1017/s1446788717000295.

Full text

Abstract:

We obtain a complete structural characterization of Cohn–Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of finitely generated projective modules is atomic and cancelative. We introduce the nonunital generalizations of graded analogs of noetherian and artinian rings, graded locally noetherian and graded locally artinian rings, and characterize graded locally noetherian and graded locally artinian Leavitt path algebras without any restriction on the cardinality of the graph. As a consequence, we relax the assumptions of the Abrams–Aranda–Perera–Siles characterization of locally noetherian and locally artinian Leavitt path algebras.

APA, Harvard, Vancouver, ISO, and other styles

8

MESYAN, ZACHARY, and LIA VAŠ. "TRACES ON SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS." Glasgow Mathematical Journal 58, no. 1 (July 21, 2015): 97–118. http://dx.doi.org/10.1017/s0017089515000087.

Full text

Abstract:

AbstractThe trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying traces on (contracted) semigroup rings over commutative rings. We show that every such ring admits a minimal trace (i.e., one that vanishes only on sums of commutators), classify all minimal traces on these rings, and give applications to various classes of semigroup rings and quotients thereof. We then study traces on Leavitt path algebras (which are quotients of contracted semigroup rings), where we describe all linear traces in terms of central maps on graph inverse semigroups and, under mild assumptions, those Leavitt path algebras that admit faithful traces.

APA, Harvard, Vancouver, ISO, and other styles

9

Bell, Jason P., T. H. Lenagan, and Kulumani M. Rangaswamy. "Leavitt path algebras satisfying a polynomial identity." Journal of Algebra and Its Applications 15, no. 05 (March 30, 2016): 1650084. http://dx.doi.org/10.1142/s0219498816500845.

Full text

Abstract:

Leavitt path algebras [Formula: see text] of an arbitrary graph [Formula: see text] over a field [Formula: see text] satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When [Formula: see text] is a finite graph, [Formula: see text] satisfying a polynomial identity is shown to be equivalent to the Gelfand–Kirillov dimension of [Formula: see text] being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph [Formula: see text], the Leavitt path algebra [Formula: see text] has Gelfand–Kirillov dimension zero if and only if [Formula: see text] has no cycles. Likewise, [Formula: see text] has Gelfand–Kirillov dimension one if and only if [Formula: see text] contains at least one cycle, but no cycle in [Formula: see text] has an exit.

APA, Harvard, Vancouver, ISO, and other styles

10

Pino, G. Aranda, K. M. Rangaswamy, and M. Siles Molina. "Generalized Regularity Conditions for Leavitt Path Algebras over Arbitrary Graphs." Communications in Algebra 42, no. 1 (October 18, 2013): 325–31. http://dx.doi.org/10.1080/00927872.2012.714026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Aranda Pino, Gonzalo, Kulumani M. Rangaswamy, and Mercedes Siles Molina. "Weakly Regular and Self-Injective Leavitt Path Algebras Over Arbitrary Graphs." Algebras and Representation Theory 14, no. 4 (August 6, 2010): 751–77. http://dx.doi.org/10.1007/s10468-010-9215-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Rangaswamy, Kulumani M. "The theory of prime ideals of Leavitt path algebras over arbitrary graphs." Journal of Algebra 375 (February 2013): 73–96. http://dx.doi.org/10.1016/j.jalgebra.2012.11.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Rangaswamy, Kulumani M. "On Generators of Two-Sided Ideals of Leavitt Path Algebras over Arbitrary Graphs." Communications in Algebra 42, no. 7 (March 13, 2014): 2859–68. http://dx.doi.org/10.1080/00927872.2013.765008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Clark, Lisa O., Benjamin Steinberg, and Daniel W. van Wyk. "GCR and CCR Steinberg Algebras." Canadian Journal of Mathematics 72, no. 6 (August 23, 2019): 1581–606. http://dx.doi.org/10.4153/s0008414x19000415.

Full text

Abstract:

AbstractKaplansky introduced the notions of CCR and GCR $C^{\ast }$-algebras, because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR $C^{\ast }$-algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.

APA, Harvard, Vancouver, ISO, and other styles

15

Hazrat, Roozbeh, and Lia Vaš. "K-theory classification of graded ultramatricial algebras with involution." Forum Mathematicum 31, no. 2 (March 1, 2019): 419–63. http://dx.doi.org/10.1515/forum-2017-0268.

Full text

Abstract:

AbstractWe consider a generalization {K_{0}^{\operatorname{gr}}(R)} of the standard Grothendieck group {K_{0}(R)} of a graded ring R with involution. If Γ is an abelian group, we show that {K_{0}^{\operatorname{gr}}} completely classifies graded ultramatricial {*}-algebras over a Γ-graded {*}-field A such that (1) each nontrivial graded component of A has a unitary element in which case we say that A has enough unitaries, and (2) the zero-component {A_{0}} is 2-proper ({aa^{*}+bb^{*}=0} implies {a=b=0} for any {a,b\in A_{0}}) and {*}-pythagorean (for any {a,b\in A_{0}} one has {aa^{*}+bb^{*}=cc^{*}} for some {c\in A_{0}}). If the involutive structure is not considered, our result implies that {K_{0}^{\operatorname{gr}}} completely classifies graded ultramatricial algebras over any graded field A. If the grading is trivial and the involutive structure is not considered, we obtain some well-known results as corollaries. If R and S are graded matricial {*}-algebras over a Γ-graded {*}-field A with enough unitaries and {f:K_{0}^{\operatorname{gr}}(R)\to K_{0}^{\operatorname{gr}}(S)} is a contractive {\mathbb{Z}[\Gamma]}-module homomorphism, we present a specific formula for a graded {*}-homomorphism {\phi:R\to S} with {K_{0}^{\operatorname{gr}}(\phi)=f}. If the grading is trivial and the involutive structure is not considered, our constructive proof implies the known results with existential proofs. If {A_{0}} is 2-proper and {*}-pythagorean, we also show that two graded {*}-homomorphisms {\phi,\psi:R\to S} are such that {K_{0}^{\operatorname{gr}}(\phi)=K_{0}^{\operatorname{gr}}(\psi)} if and only if there is a unitary element u of degree zero in S such that {\phi(r)=u\psi(r)u^{*}} for any {r\in R}. As an application of our results, we show that the graded version of the Isomorphism Conjecture holds for a class of Leavitt path algebras: if E and F are countable, row-finite, no-exit graphs in which every infinite path ends in a sink or a cycle and K is a 2-proper and {*}-pythagorean field, then the Leavitt path algebras {L_{K}(E)} and {L_{K}(F)} are isomorphic as graded rings if any only if they are isomorphic as graded {*}-algebras. We also present examples which illustrate that {K_{0}^{\operatorname{gr}}} produces a finer invariant than {K_{0}}.

APA, Harvard, Vancouver, ISO, and other styles

16

Rangaswamy, Kulumani M. "On graded primitive leavitt path algebras." Journal of Algebra and Its Applications, July 17, 2020, 2150173. http://dx.doi.org/10.1142/s0219498821501735.

Full text

Abstract:

Graded primitive Leavitt path algebras of arbitrary directed graphs over a field [Formula: see text] are completely characterized by means of graphical conditions. Necessary and sufficient conditions are given under which a graded prime Leavitt path algebra becomes graded primitive and this leads to answering the graded version of a question of Kaplansky on von Neumann regular prime rings in the context of Leavitt path algebras.

APA, Harvard, Vancouver, ISO, and other styles

17

Kanwar, Pramod, Meenu Khatkar, and R. K. Sharma. "ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS." International Electronic Journal of Algebra, July 11, 2019, 191–203. http://dx.doi.org/10.24330/ieja.587053.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Soumitra Das and Ardeline M. Buhphang. "Principally-Injective Leavitt Path Algebras over Arbitrary Graphs." Journal of Mathematics and System Science 9, no. 3 (March 28, 2019). http://dx.doi.org/10.17265/2159-5291/2019.03.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!