On Basic Ideal Generated by Vertices in Cycles without Exits in Leavitt Path Algebras

Vertices located on cycles without exits have a role in constructing ideals in the Leavitt path algebras over a commutative unital ring. One key reason is that the set of such vertices is hereditary. In addition, an ideal of the commutative unital ring can be combined with these vertices to form an ideal in the Leavitt path algebra. This article focuses on creating a (basic) ideal in the Leavitt path algebras, which is generated by vertices on cycles without exits.