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Leavitt path algebras with coefficients in a Clifford semifield

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1 Published in 2019 at "Communications in Algebra"

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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1 Published in 2019 at "Communications in Algebra"

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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1 Published in 2018 at "Transactions of the American Mathematical Society"

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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1 Published in 2019 at "Journal of Algebra and Its Applications"

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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1 Published in 2018 at "Filomat"

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