循环半群及其矩阵表示  

Monogenic Semigroups and their Matrix Presentations

作　　者：徐诚慷 周彪 石黄萍 

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《上饶师范学院学报》2017年第6期1-4,共4页Journal of Shangrao Normal University

基　　金：数学天元基金项目(11656157);江西省教育厅科技项目(GJJ161044)

摘　　要：循环群在群同构意义下只有两类,即整数加法群和整数模n剩余类群。证明了循环半群共有6类,其中无限循环半群有整数加法群、非负整数加法半群和正整数加法半群这三类,而有限循环半群也只有三类:整数模n剩余类群,还有两类变换半群。更进一步,对有限循环半群给出两个矩阵表示。There are only two different isomorphic classes of cyclic groups,the group of integers and the group of inte- gers modulo n. In this paper we prove that there are only 6 different classes of cyclic semigroups in the sense of iso- morphism,of which the three infinite classes are the group of integers , the semigroup of non-negative integers and the semigroup of positive integers,the three finite classes are the group of integers modulo n,and two transformation sem- igroups. Moreover,two matrix presentations for the finite cyclic semigroups are given.

关 键 词：半群 循环半群 矩阵表示 

分 类 号：O152.7[理学—数学]