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
Realization for tensor products of Leavitt path algebras of hypergraphs
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DOI: 10.1080/00927872.2024.2428317
Abstract: Abstract For two given hypergraphs, we construct an augmentation hypergraph. We establish an algebra homomorphism from the Leavitt path algebra of the augmentation hypergraph to the tensor product of the corresponding Leavitt path algebras of… read more here.
Keywords: weighted leavitt; path algebras; tensor; algebra ... See more keywords
Graded simplicities of Leavitt path algebras with coefficients in Clifford semifield and k-semifield
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DOI: 10.1080/00927872.2024.2445227
Abstract: Abstract Using the natural Z-grading, Graded Simplicity and Graded Uniqueness Theorems have been obtained in the past for Leavitt path algebras over fields and commutative unital rings. In this paper we extend some of these… read more here.
Keywords: path algebras; algebra; semifield semifield; leavitt path ... 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