TYPE-A SEMIGROUPS WHOSE FULL SUBSEMIGROUPS FORM A CHAIN UNDER SET INCLUSION
Xiaojiang Guo, Fusheng Huang, K. P. Shum · Asian-European Journal of Mathematics · 2008
A semigroup S is called a ∇-semigroup if the set of all its full subsemigroups forms a chain under set inclusion. In this paper, we investigate some properties of such kind of semigroups and establish several characterization theorems of type-A ∇-semigroups. Our theorems generalize the known results of P. R. Jones obtained in 1981 on inverse semigroups whose full inverse subsemigroups form a chain.