On Two Types Of Matrix Semigroups

The theory of matrix semigroups is a very important branch of the matrix theory. Many experts and scholars thorough and systematically investigate it. In this paper, we mainly study (0,∞)-matrix semigroup and the semigroup of matrices over the finite chain K.In chapter 1. we simply introduce the background and the present state of the matrix theory; for the sake of convenience, we introduce some fundamental knowledge about semigroups and semirings. In chapter 2, firstly, we give some fundamental propositions about vector, matrix and rank overβ₀;secondly, we give many characterizations of Green-relations of (0,∞)-matrix semigroup through space and rank, respectively; and study the idempotent element and regular element of (0,∞)-matrix semigroup. In chapter 3, we discuss Green-relations of the semigroup of matrices over the finite chain K; and we give many characterizations of idempotent element of the semigroup of the matrices over the finite chain K through anchored, stable and stabilition. then we extend some results of paper [9]. In this way, we can transfer the research of some questions in Fuzzy matrix to it in the matrix over the finite chain K.