| 弱M-拟Armendariz环 |
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| 引用本文： | 解晓娟,宋贤梅.弱M-拟Armendariz环[J].安徽师范大学学报(自然科学版),2012,35(2):123-126. |
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| 作者姓名： | 解晓娟 宋贤梅 |
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| 作者单位： | 安徽师范大学数学计算机科学学院,安徽芜湖,241000;安徽师范大学数学计算机科学学院,安徽芜湖,241000 |
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| 基金项目： | 安徽省教育厅重点研究项目，安徽师范大学专项基金 |
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| 摘 要： | 本文引入了弱M-拟Armendariz环的概念,其中M是幺半群,它是M-拟Armendariz环和弱M-Armendariz环的一般推广.本文中研究了这类环的相关性质.我们证明了(1)若I是环R的半交换的理想,使得R/I是弱M-拟Armendariz环的,则R是弱M-拟Armendariz环,其中M是严格的完全序幺半群;(2)一个有限生成的Abelian群G是无挠的当且仅当存在一个环R使得R是弱G-拟Armendariz环.
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| 关 键 词： | 弱M-拟Armendariz环 M-拟Armendariz环 弱M-Armendariz环 半交换环 |
Weak M-Quasi-Armendariz Rings |
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| XIE Xiao-juan
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SONG Xian-mei.Weak M-Quasi-Armendariz Rings[J].Journal of Anhui Normal University(Natural Science Edition),2012,35(2):123-126. |
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| Authors: | XIE Xiao-juan SONG Xian-mei |
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| Institution: | (College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241003,China) |
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| Abstract: | In this paper,we define weak M-quasi-Armendariz rings which are generalization of weak M-Armendariz rings and M-quasi-Armeudariz rings,where M is a monoid.We mainly study some properties of weak M-quasiArmendariz rings.We proved that(1) if I is semicommutative ideal of ring R such that R/I is M-quasi-weak Armendariz rings,then R is M-quasi-weak Armendariz rings,where M is strictly totally ordered monoid;(2) a finitely generated Abelian group G is torsion-free if and if there exists a ring R such that R is G-quasi-weak Armendariz rings. |
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| Keywords: | weak M-quasi-Armendariz rings M-quasi-Armendariz rings weak M-Armendariz rings semi-commutative rings |
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