Soft intersection almost subsemigroups of semigroups

Abstract

Semigroups are the building blocks of algebra as they have application in automata, coding theory, formal languages, and theoretical computer science. They are also used in the solutions of graph theory and optimization theory. For the advanced study of algebraic structures and their applications, ideals are essential. The generalization of ideals in algebraic structures is necessary for further research on algebraic structures. The main purpose of this paper is to present the notion of soft intersection almost subsemigroup of a semigroup, which is a generalization of soft intersection subsemigroup and investigate its basic properties in detail. In this context, we also obtain many striking relationships between almost subsemigroups and soft intersection almost subsemigroups concerning minimality, primeness, semiprimeness and strongly primeness.

Keywords: semigroups, soft intersection, algebraic structures, almost subsemigroup of a semigroup, graph theory, optimization theory, minimality, simplicity, semi-simplicity and strong simplicity.