ON LEAVITT PATH ALGEBRAS OVER COMMUTATIVE RINGS

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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