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

Article type: Research Article

Authors: Kar, Sukhendu | Purkait, Sudipta

Affiliations: Department of Mathematics, Jadavpur University, Kolkata, India

Note: [] Corresponding author. Sukhendu Kar, Department of Mathematics, Jadavpur University, 188, Raja S.C. Mallick Road, Kolkata–700032, India. E-mails: [email protected] (Sukhendu Kar), [email protected] (Sudipta Purkait).

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.

Keywords: Power fuzzy semiring, fuzzy generalized k-bi-ideal, fuzzy interior k-ideal, k-regular semiring, k-intra-regular semiring

DOI: 10.3233/IFS-141266

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 6, pp. 3089-3101, 2014