(M, N)-Soft Intersection Nearsemirings and (M, N)-α-Inclusion Along with Its Algebraic Applications

Abstract

In this note, we introduce (M, N)-soft intersection nearsemirings (abbreviate as (M, N)-SI-nearsemirings) by utilizing the intersection operation of sets. We study the set theoretic characteristics of (M, N)-Soft intersection nearsemirings with the effects of different types of sets operations. (M, N)-SI-subnearsemirings, (M, N)-SI-ideals, and (M, N)-SI-c-ideals are also introduced and discussed. Furthermore, we introduce the notions of (M, N)-α-inclusion, soft uni-int c-products, soft uni-int c-sums and study (M, N)-SI-nearsemirings by using these operations. We also inter-relate (M, N)-SI-nearsemirings and classical nearsemirings by utilizing (M, N)-α-inclusion.