The Jacobson radical types of Leavitt path algebras with coefficients in a commutative unital semiring

Abstract

In this paper, we calculate the J - radical and Js - radical of the Leavitt path algebras with coefficients in a commutative semiring of some finite graphs. In particular, we calculate J - radical and Js - radical of the Leavitt path algebras with coefficients in a field of acyclic graphs, no-exit graphs and give applicable examples.