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Principally-Injective Leavitt Path Algebras over Arbitrary Graphs
Soumitra Das and Ardeline M. Buhphang
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DOI:10.17265/2159-5291/2019.03.002
Department of Mathematics, North-Eastern Hill University, Permanent Campus, Shillong 793022, Meghalaya, India
A ring R is called right principally-injective if every R-homomorphism f: aR → R, a ∈ R, extends to R, or equivalently, if every system of equations xa = b (a, b ∈ R) is solvable in R. In this paper we show that for any arbitrary graph E and for a field K, principally-injective conditions for the Leavitt path algebra LK(E) are equivalent to that graph E being acyclic. We also show that the principally-injective Leavitt path algebras are precisely the von Neumann regular Leavitt path algebras.
Leavitt path algebras, von Neumann regular rings, principally-injective rings, arbitrary graph.
Das, S. 2019. “Principally-Injective Leavitt Path Algebras over Arbitrary Graphs” Journal of Mathematics and System Science 9: 86-9.
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