Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C⁎-algebras
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DOI: 10.1016/j.jalgebra.2021.11.004
Abstract: We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph $E$ with coefficients in a field $K$ is isomorphic to a Steinberg… read more here.
Keywords: algebra; leavitt path; graph; isomorphic steinberg ... See more keywords
FP-injective semirings, semigroup rings and Leavitt path algebras
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DOI: 10.1080/00927872.2016.1226862
Abstract: ABSTRACT In this paper we give characterisations of FP-injective semirings (previously termed “exact” semirings in work of the first author). We provide a basic connection between FP-injective semirings and P-injective semirings, and establish that FP-injectivity… read more here.
Keywords: semirings semigroup; injective semirings; leavitt path; semigroup rings ... See more keywords
Leavitt path algebras with coefficients in a Clifford semifield
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DOI: 10.1080/00927872.2018.1492589
Abstract: Abstract In this article, we define the Leavitt path algebra of a directed graph Γ with coefficients in a Clifford semifield S. The general properties of are briefly discussed. Then, concentrating on the full k-simplicity… read more here.
Keywords: path algebras; clifford semifield; leavitt path; algebras coefficients ... See more keywords
Bases of Leavitt path algebras with only strongly regular elements
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DOI: 10.1080/00927872.2018.1552283
Abstract: Abstract Recent articles consider invertible and locally invertible algebras (respectively, those having a basis consisting solely of invertible or solely of strongly regular elements). Previous contributions to the subject include the study of when Leavitt… read more here.
Keywords: path algebras; leavitt path; strongly regular; bases leavitt ... See more keywords
Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras
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DOI: 10.1090/tran/7460
Abstract: We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit… read more here.
Keywords: steinberg algebras; path algebras; ideals steinberg; strongly effective ... See more keywords
Cohn–Leavitt path algebras and the invariant basis number property
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DOI: 10.1142/s0219498819500865
Abstract: We give the necessary and sufficient condition for a separated Cohn–Leavitt path algebra of a finite digraph to have Invariant Basis Number (IBN). As a consequence, separated Cohn path algebras have IBN. We determine the… read more here.
Keywords: invariant basis; path algebras; leavitt path; path ... See more keywords
On endomorphism rings of Leavitt path algebras
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DOI: 10.2298/fil1804175o
Abstract: Let E be an arbitrary graph, K be any field and A be the endomorphism ring of L := LK(E) considered as a right L-module. Among the other results, we prove that: (1) if A… read more here.
Keywords: endomorphism rings; leavitt path; path algebras; rings leavitt ... See more keywords