A Generalization of m-Bi-Ideals in b-Semirings and Its Characterizing Extension

In this study, we introduce new types of m-quasi-ideals and m-bi-ideals in b-semirings and provide some characterizations of these ideals. We use an algebraic method to express the fundamental properties of m-bi-ideals in b-semirings. We also discuss the m-ideals in terms of their algebraic structures. Moreover, we examine the m-bi-ideals and their generators and provide some characterizations regarding bi-ideals. We further discuss the m-bi-ideal generated by a non-empty subset S, which is denoted by <S>m= S∪Σfinite BSmB, where B is the set of all bi-ideals.