全正则子半群构成链的正则半群

摘要

本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全o-单半群的结构.%The main aim of this paper is to study regular semigroups whose full regular subsemigroups form a chain. We obtain a sufficient and necessary condition for a regular semigroup whose full regular subsemigroups form a chain. This extends the related result of Jones on inverse semigroups. In addition, the structure of completely O-simple semigroups whose full regular subsemigroups form a chain is established.