The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey

DOI10.1007/978-3-030-43416-8_16zbMath1440.16032arXiv1902.00774OpenAlexW3167101064MaRDI QIDQ5119704

Kulumani M. Rangaswamy

Publication date: 1 September 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00774

zbMATH Keywords

Leavitt path algebrasmultiplicative ideal theoryfactorization of ideals

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Leavitt path algebras (16S88) Modules, bimodules and ideals in associative algebras (16D99)

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Cites Work

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• The theory of prime ideals of Leavitt path algebras over arbitrary graphs.
• Factoring ideals in integral domains
• Morita equivalence for rings without identity
• Ideals in graph algebras
• Leavitt path algebras are Bézout
• Ideal theory in Prüfer domains -- an unconventional approach
• The multiplicative ideal theory of Leavitt path algebras
• Leavitt path algebras
• Uniqueness theorems and ideal structure for Leavitt path algebras
• Graded Rings and Graded Grothendieck Groups
• Leavitt path algebras of separated graphs
• On Prüfer-like properties of Leavitt path algebras
• Commutative ideal theory without finiteness conditions: Completely irreducible ideals
• Commutative ideal theory without finiteness conditions: Primal ideals
• Chains of semiprime and prime ideals in Leavitt path algebras
• On Generators of Two-Sided Ideals of Leavitt Path Algebras over Arbitrary Graphs

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