ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS

Year 2019, Volume: 26 Issue: 26, 191 - 203, 11.07.2019

Pramod KANWAR Meenu KHATKAR R. K. SHARMA

https://doi.org/10.24330/ieja.587053

Cited By: 1

Abstract

In this article, basic ideals in a Leavitt path algebra over a com-

mutative unital ring are studied. It is shown that for a nite acyclic graph E

and a commutative unital ring R, the Leavitt path algebra LR(E) is a direct

sum of minimal basic ideals and that for a commutative ring R and a graph

E satisfying Condition (L), the Leavitt path algebra LR(E) has no non-zero

nilpotent basic ideals. Uniqueness theorems for Leavitt path algebras over

commutative unital rings are also discussed.

Keywords

Leavitt path algebra, basic ideal, minimal basic ideal, uniqueness theorem

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