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.