Rees矩阵半群的GK-维数  

Gelfand-Kirillov Dimensions of Rees matrix semigroups

作　　者：崔冉冉[1] 孟庆云[1] CUI Ranran;MENG Qingyun(College of Science,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]河南工业大学理学院,河南郑州450001

出　　处：《纯粹数学与应用数学》2023年第2期294-302,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11601121);河南省自然科学基金(162300410066);西安市科技计划项目(2020KJRC0092).

摘　　要：主要探讨Rees矩阵半群的GK-维数问题.首先刻画Rees矩阵半群的性质,含有零元的一类Rees矩阵半群S的GK-维数等于S的任意非零极大幺半群M的GK-维数.然后利用这些性质,证明一类Rees矩阵半群S有多项式增长当且仅当S的所有的子幺半群有多项式增长,推广了本原富足半群里的相关结果.Gelfand-Kirillov dimensions of some Rees matrix semigroups are investigated.First some properties of Rees matrix semigroups are given.The GK-dimension of some certain Rees matrix semigroup S with 0,equals the GK-dimension of M,which is any nonzero maximal monoid of S.Then by using the properties,it is shown that for certain Rees matrix semigroup S,S has polynomial growth if and only if all of its submonoids M have polynomial growth.It is an extend work of the results of some primitive semigroup algebras.

关 键 词：GK-维数 REES矩阵半群 本原正则半群 线性增长 

分 类 号：O152.7[理学—数学]