Feeble ring

Abstract

An ideal A of a semiring S is called k-ideal if for any two elements r∈A and x∈S such that r+x∈A, then x∈Aʺ. This leads us to introduce the new concept feeble ring as generalization of k-ideal. Several basic properties, example and characterization of this concept are given. Moreover, the study investigate relationship of feeble ring with other classes.