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弱M—Armendariz环
  • ISSN号：1003-7985
  • 期刊名称：《东南大学学报：英文版》
  • 时间：0
  • 分类：O153.3[理学—数学;理学—基础数学]
  • 作者机构：[1]东南大学数学系,南京210096, [2]西北师范大学数学系,兰州730070
  • 相关基金：Foundation items： The National Natural Science Foundation of China （ No. 10571026）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （No. 20060286006）.
作者： 张翠萍[1,2], 陈建龙[1]
关键词： 半交换环, M-Armendariz环, 弱ARMENDARIZ环, 弱M—Armendariz环, semicommutative rings, M-Armendariz rings, weak Armendariz rings, weak M-Armendariz rings
中文摘要：

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：尺是弱M-Armendariz环当且仅当对任意的n，R的n阶上三角矩阵环瓦（R）是弱M-Armendariz环；如果，是环尺的半交换理想，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；如果尺是半交换的M-Armendariz环，则R是弱M×N-Armendariz环，其中Ⅳ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尺，使得尺是弱G—Armendariz环．

英文摘要：

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.

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期刊信息
  • 《东南大学学报：英文版》
  • 主管单位:教育部
  • 主办单位:东南大学
  • 主编：毛善锋
  • 地址：南京市四牌楼2号
  • 邮编：210096
  • 邮箱：xuebao@seu.edu.cn
  • 电话：025-83794323 83794343传
  • 国际标准刊号：ISSN：1003-7985
  • 国内统一刊号：ISSN：32-1325/N
  • 邮发代号:
  • 获奖情况:
  • 2010年和2012年荣获第三届和第四届中国高校优秀科...
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  • 被引量:493