由正则子半群所决定的半群上子半群格的结构

The Structure of the Lattice of All Subsemigroups on a Semigroup Determined by Its Regular Subsemigroups

本文中提出了半群上的正则子半群的概念,通过半群上的正则子半群给出了半群上的一般子半群的表示,进而研究了半群上的子半群格成为完全分配格的几个充要条件。同时,对比正则性更为广义的紧致性也作了一般探讨。

The concept of regular subsemigroup on a semigroup presented in the paper is used to give a general formula for a general subsemigroup. Some conditions under which the lattice of all subsemigroups on a semigroup will be a complete distributive lattice are investigated.The compactness that is more general than regularity is also examined.