Characterization of some k-regularities of semirings in terms of fuzzy ideals of semirings

Abstract

The notion of k-regularity in a semiring generalizes the notion of a regular ring introduced by J. Von Neumaan [15]. In semiring theory, the notion of k-regularity was extensively studied by Sen and Bhuniya [17]. In this paper, we study the concept of k-regularities of a semiring in fuzzy setting and characterize some k-regularities of semirings by using different fuzzy ideals of semirings. We also introduce the concept of power fuzzy semirings and study the notion of k-regularities of power fuzzy semirings with the help of regularities of semigroups.