Power Semigroups of a Class of Clifford Semigroups

DOI：10.3770/j.issn:2095-2651.2014.01.007

 作者 单位 胡兰兰 江西师范大学数学与信息科学学院, 江西 南昌 330022 甘爱萍 江西师范大学数学与信息科学学院, 江西 南昌 330022

设$S=\bigcup (G_{\alpha}: \alpha\in E)$是群的半格(即Clifford半群)及$n$是自然数.若$E$是$n$-元链, 则称$S$是群的$n$元链.记$\mathcal{C}_{n}$为所有群的$n$元链所构成的集合.本文我们将证明对任意自然数$n$,半群类$\mathcal{C}_{n}$均满足强同构性质.

Let $S=\bigcup (G_{\alpha}: \alpha\in E)$ be a semilattice of groups (i.e., a Clifford semigroup) and $n$ a natural number. $E$ is called an $n$-element chain of groups if it is an $n$-element chain. Denote by $\mathcal{C}_{n}$ the set of all $n$-element chains of groups. In this paper we shall show that for any natural number $n$, the class of semigroups $\mathcal{C}_{n}$ satisfies the strong isomorphism property.