On Generators of Two-Sided Ideals of Leavitt Path Algebras over Arbitrary Graphs

DOI10.1080/00927872.2013.765008zbMath1300.16006OpenAlexW2020368396MaRDI QIDQ5417951

Kulumani M. Rangaswamy

Publication date: 23 May 2014

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

Full work available at URL: https://doi.org/10.1080/00927872.2013.765008

zbMATH Keywords

generators of nongraded idealssystems of generators of Leavitt path algebras

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) 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) Representations of quivers and partially ordered sets (16G20) Ideals in associative algebras (16D25)

Related Items

Leavitt path algebras are Bézout ⋮ A note on the regular ideals of Leavitt path algebras ⋮ On intersections of two-sided ideals of Leavitt path algebras ⋮ Products and intersections of prime-power ideals in Leavitt path algebras ⋮ Annihilator ideals of graph algebras ⋮ Products of ideals in Leavitt path algebras ⋮ Unnamed Item ⋮ The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey ⋮ A Survey of Some of the Recent Developments in Leavitt Path Algebras ⋮ A Survey on the Ideal Structure of Leavitt Path Algebras ⋮ Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras ⋮ On Prüfer-like properties of Leavitt path algebras ⋮ On graded primitive Leavitt path algebras ⋮ Existence of maximal ideals in Leavitt path algebras ⋮ The multiplicative ideal theory of Leavitt path algebras ⋮ The talented monoid of a Leavitt path algebra ⋮ Chains of semiprime and prime ideals in Leavitt path algebras ⋮ Prüfer modules over Leavitt path algebras ⋮ Leavitt \(R\)-algebras over countable graphs embed into \(L_{2,R}\).

Cites Work

• The theory of prime ideals of Leavitt path algebras over arbitrary graphs.
• Socle theory for Leavitt path algebras of arbitrary graphs.
• Nonstable \(K\)-theory for graph algebras.
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The Leavitt path algebra of a graph.
• TWO-SIDED IDEALS IN LEAVITT PATH ALGEBRAS
• Prime spectrum and primitive Leavitt path algebras

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