ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS

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International Electronic Journal of Algebra
Volume:26 Issue:26
ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS

ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS

Authors : Pramod KANWAR, Meenu KHATKAR, R K SHARMA

Pages : 191-203

Doi:10.24330/ieja.587053

View : 16 | Download : 11

Publication Date : 2019-07-11

Article Type : Research Paper

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 LRinsert ignore into journalissuearticles values(E); is a direct sum of minimal basic ideals and that for a commutative ring R and a graph E satisfying Condition insert ignore into journalissuearticles values(L);, the Leavitt path algebra LRinsert ignore into journalissuearticles values(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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