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Chain Conditions for Epsilon-Strongly Graded Rings with Applications to Leavitt Path Algebras
Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.ORCID-id: 0000-0001-8445-3936
2019 (engelsk)Inngår i: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079Artikkel i tidsskrift (Fagfellevurdert) Epub ahead of print
Abstract [en]

Let G be a group with neutral element e and let S=⊕g∈GSg be a G-graded ring. A necessary condition for S to be noetherian is that the principal component Se is noetherian. The following partial converse is well-known: If S is strongly-graded and G is a polycyclic-by-finite group, then Se being noetherian implies that S is noetherian. We will generalize the noetherianity result to the recently introduced class of epsilon-strongly graded rings. We will also provide results on the artinianity of epsilon-strongly graded rings. As our main application we obtain characterizations of noetherian and artinian Leavitt path algebras with coefficients in a general unital ring. This extends a recent characterization by Steinberg for Leavitt path algebras with coefficients in a commutative unital ring and previous characterizations by Abrams, Aranda Pino and Siles Molina for Leavitt path algebras with coefficients in a field. Secondly, we obtain characterizations of noetherian and artinian unital partial crossed products. © 2019, The Author(s).

sted, utgiver, år, opplag, sider
Springer Netherlands , 2019.
Emneord [en]
Chain conditions, Epsilon-strongly graded ring, Group graded ring, Leavitt path algebra, Partial crossed product, Mathematical techniques, Chain condition, Finite groups, Neutral elements, Path algebras, Principal Components, Algebra
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Identifikatorer
URN: urn:nbn:se:bth-18607DOI: 10.1007/s10468-019-09909-0Scopus ID: 2-s2.0-85068819896OAI: oai:DiVA.org:bth-18607DiVA, id: diva2:1349795
Tilgjengelig fra: 2019-09-10 Laget: 2019-09-10 Sist oppdatert: 2019-09-10

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