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Simplicity of Leavitt Path Algebras via Graded Ring Theory
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-37179 Karlskrona (SWE).
2023 (English)In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 108, no 3, p. 428-437Article in journal (Refereed) Published
Abstract [en]

Suppose that R is an associative unital ring and that E= (E-0, E-1, r, s) is a directed graph. Using results from graded ring theory, we show that the associated Leavitt path algebra L-R(E) is simple if and only if R is simple, E-0 has no nontrivial hereditary and saturated subset, and every cycle in E has an exit. We also give a complete description of the centre of a simple Leavitt path algebra.

Place, publisher, year, edition, pages
Cambridge University Press, 2023. Vol. 108, no 3, p. 428-437
Keywords [en]
Leavitt path algebra; graded ring; simple ring; centre
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:hv:diva-19848DOI: 10.1017/S0004972723000114ISI: 000943276000001Scopus ID: 2-s2.0-85177820296OAI: oai:DiVA.org:hv-19848DiVA, id: diva2:1821747
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Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2023-12-20

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Lundström, Patrik

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