Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring

DOI10.1080/00927872.2014.946133zbMath1333.16009arXiv1202.5478OpenAlexW1874680683MaRDI QIDQ3448557

Hossein Larki

Publication date: 26 October 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5478

zbMATH Keywords

prime idealsprimitive idealsLeavitt path algebrasgraded idealsbasic ideals

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) General theory of (C^*)-algebras (46L05) Representations of quivers and partially ordered sets (16G20) Graded rings and modules (associative rings and algebras) (16W50) Ideals in associative algebras (16D25) Leavitt path algebras (16S88)

Related Items

Prime and primitive Kumjian–Pask algebras ⋮ Leavitt path algebras of edge-colored graphs. ⋮ Purely infinite simple Kumjian-Pask algebras ⋮ Basic One-Sided Ideals of Leavitt Path Algebras over Commutative Rings ⋮ Generalized quasi-Baer *-rings and Banach *-algebras ⋮ A taxonomy of Dedekind-finite and reflexive rings ⋮ Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras ⋮ Unnamed Item ⋮ Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras ⋮ A classification of ideals in Steinberg and Leavitt path algebras over arbitrary rings ⋮ The Leavitt Path Algebras of Ultragraphs

Cites Work

• Leavitt path algebras with coefficients in a commutative ring.
• Ideals in graph algebras
• Exchange Leavitt path algebras and stable rank
• Finite-dimensional Leavitt path algebras.
• Locally finite Leavitt path algebras.
• A class of C*-algebras and topological Markov chains
• The primitive ideal space of the \(C^*\)-algebra of infinite graphs
• Nonstable \(K\)-theory for graph algebras.
• The socle of a Leavitt path algebra.
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The \(C^*\)-algebras of arbitrary graphs
• The Leavitt path algebra of a graph.
• Stabe rank of graph algebras: Type I graph algebras and their limits
• Prime spectrum and primitive Leavitt path algebras
• The ideal structure of Cuntz–Krieger algebras
• Chain conditions for Leavitt path algebras

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