相对于幺半群的α-斜Armendariz环

doi:10.6040/j.issn.1671-9352.0.2015.213

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 1-5.doi: 10.6040/j.issn.1671-9352.0.2015.213

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相对于幺半群的α-斜Armendariz环

耿道宏¹,王尧¹,任艳丽^2*

1.南京信息工程大学数学与统计学院, 江苏南京 210044;2.南京晓庄学院数学与信息技术学院, 江苏南京 211171

收稿日期:2015-05-02 出版日期:2016-02-16 发布日期:2016-03-11
通讯作者: 任艳丽(1965— ), 女, 硕士, 教授, 研究方向为环论. E-mail:renyanlisx@163.com E-mail:gengdaohong@163.com
作者简介:耿道宏(1991— ), 男, 硕士, 研究方向为环论. E-mail:gengdaohong@163.com
基金资助:
国家自然科学基金资助项目(41275117);江苏省自然科学基金资助项目(BK20141476)

α-skew Armendariz rings relative to a monoid

GENG Dao-hong¹, WANG Yao¹, REN Yan-li^2*

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
2. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China

Received:2015-05-02 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 引入了α-斜M-Armendariz环的概念。讨论了α-斜M-Armendariz环与相关环的关系,证明了在α-斜M-Armendariz环条件下,Baer环(右p.p.-环,右zip环)的斜幺半群环扩张仍然是Baer环(右p.p.-环,右zip环)。

关键词: p.p.-环, Baer环, zip环, α-斜M-Armendariz环, 斜幺半群环

Abstract: The concept of α-skew M-Armendariz rings is introduced. The relationship between α-skew M-Armendariz rings and related rings is investigated, and it is proved that the skew monoid ring extension of a Baer ring(right p.p.-ring, right zip ring)is a Baer ring(right p.p.-ring, right zip ring)in case the ring is an α-skew M-Armendariz.

Key words: skew monoid ring, Baer ring, α-skew M-Armendariz ring, zip ring, p.p.-ring

中图分类号:

O153.3

耿道宏,王尧,任艳丽. 相对于幺半群的α-斜Armendariz环[J]. 山东大学学报（理学版）, 2016, 51(2): 1-5.

GENG Dao-hong, WANG Yao, REN Yan-li. α-skew Armendariz rings relative to a monoid[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 1-5.

参考文献

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[3] LIU Zhongkui. Armendariz rings relative to a monoid[J]. Comm Algebra, 2005, 33(3):649-661.
[4] OUYANG Lunqun. On weak annihilator ideals of skew monoid rings[J]. Comm Algebra, 2011, 39(11):4259-4272.
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[8] CORTES W. Skew polynomial extensions over zip rings[J]. Int J Math Sci, 2008, 9(10):1-9.

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相对于幺半群的α-斜Armendariz环

α-skew Armendariz rings relative to a monoid

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