Weak M-Armendariz rings  

弱M-Armendariz环(英文)

作　　者：张翠萍[1,2] 陈建龙[1] 

机构地区：[1]东南大学数学系,南京210096 [2]西北师范大学数学系,兰州730070

出　　处：《Journal of Southeast University(English Edition)》2009年第1期142-146,共5页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China (No.10571026);the Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20060286006)

摘　　要：For a monoid M, this paper introduces the weak M- Armendariz rings which are a common generalization of the M- Armendariz rings and the weak Armendariz rings, and investigates their properties. Moreover, this paper proves that： a ring R is weak M-Armendariz if and only if for any n, the n-by-n upper triangular matrix ring Tn （R） over R is weak M- Armendariz; if I is a semicommutative ideal of ring R such that R/I is weak M-Armendariz, then R is weak M-Armendariz, where M is a strictly totally ordered monoid; if a ring R is semicommutative and M-Armendariz, then R is weak M × N- Armendariz, where N is a strictly totally ordered monoid; a finitely generated Abelian group G is torsion-free if and only if there exists a ring R such that R is weak G-Armendariz.对于幺半群M,引入了弱M-Armendariz环的概念,此概念是M-Armendariz环和弱Armendariz环的共同推广.研究了这类环的性质,并且证明了:R是弱M-Armendariz环当且仅当对任意的n,R的n阶上三角矩阵环Tn(R)是弱M-Armendariz环;如果I是环R的半交换理想,使得R/I是弱M-Armendariz环,则R是弱M-Armendariz环,其中M是严格全序幺半群;如果R是半交换的M-Armendariz环,则R是弱M×N-Armendariz环,其中N是严格全序幺半群;有限生成Abelian群G是torsion-free的当且仅当存在一个环R,使得R是弱G-Armendariz环.

关 键 词：semicommutative rings M-Armendariz rings weak Armendariz rings weak M-Armendariz rings 

分 类 号：O153.3[理学—数学]