Certain Regular Semigroups of Infinite Matrices

S. Pianskool, P. Lertwichitsilp, K. Savettaraseranee

Abstract

Let F be a field and N the set of natural numbers. It is known that the multiplicative semigroup of all bounded $N x N$ matrices over F is a regular semigroup. Our purpose is to consider the multiplicative semigroup U*(F) of all column bounded upper triangular $N x N$ matrices A over F with for some $k \in N$, $ and $A_{ij} = 0$ for i > k and all $j \in N$. In this paper, we show that U*(F) is a regular semigroup which is a disjoint union of right simple regular semigroups, and its idempotents are also determined.