Fuzzy k-Ideals of Semirings

Abstract

This chapter consists of eight sections. In section 1 we prove that the k-sum and k-product of fuzzy k-ideals of a semiring is a fuzzy k-ideal. section 2 is devoted to characterizing k-regular semirings in terms of fuzzy left (right) k-ideals. Section 3 contains various characterizations of right k-weakly regular semirings by fuzzy right k-ideals. In section 4, we define fuzzy prime and semiprime right k-ideals and it is shown that R is a right k-weakly regular semiring if and only if each fuzzy right kideal of R is semiprime. In section 5, we characterize semirings in which each fuzzy k-ideal is idempotent and section 6 presents some results on prime and semiprime fuzzy k-ideals. We then study ”k-semirings” and present some results related to these semirings. Finally, Section 8 is devoted to a study of fuzzy congruences of semirings.