Emerging Theorems: An Amalgamative Outcome of Simple, 0-Simple, Semigroups, Principal factors an Expounding Assortment and Automation of semi-groups with space valued Fuzzy weakly inside principles

Abstract

Before tackling the question we should perhaps begin by saying what a semigroup is. A non-empty set S endowed with a single binary operation is known as a semigroup if for evey x,y,z [2][3]in S, If in addition there exists 1 in S such that, for every x in S, we say that S is a semigroup with identity or (more usually) a monoid. In this article, we give a definition of an space valued fuzzy weakly inside ideal. We study some interesting properties [4] [5] [6] of space valued fuzzy weakly inside ideals and the relationship between space valued fuzzy weakly interior ideals and space valued fuzzy principles. We characterize some semigroups by using interval valued fuzzy weakly interior principles. Moreover, we found theorems of the homorphic image and the preimage of an space valued fuzzy weakly inside principle in semigroups [7]. The 0-simple semigroups begins with some elementary results on simple and 0-simple semigroups and a decomposition theorem for semigroups in general that indicates why and understanding of simple and 0-simple semigroups is important. The main result of the chapter is a structure theorem due to Rees (1940) [2, 31] which applies to 0-simple semigroups satisfying both the minimal conditions -- what are called completely 0-simple semigroups. Rees himself used a different definition, but we shall see below theorems that the two definitions are equivalent [1].