MATRIX REPRESENTATIONS OF AMPLE SEMIGROUPS
Xiaojiang Guo, K. P. Shum · Journal of Algebra and Its Applications · 2013
An adequate semigroup S is said to be ample if for any e2 = e, a ∈ S, ae = (ae)†a and ea = a(ea)*. It is well known that inverse semigroups are ample semigroups. The purpose of this paper is to study matrix representations of an ample semigroup. Some properties of ample semigroups are obtained. It is proved that any indecomposable good matrix representations of an ample semigroup can be constructed by using those of weak Brandt semigroups.