On leavitt path algebras over commutative rings

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© 2019, Hacettepe University. All rights reserved. In this article, basic ideals in a Leavitt path algebra over a commutative unital ring are studied. It is shown that for a finite 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.