幂级数弱McCoy环

doi:10.6040/j.issn.1671-9352.0.2015.150

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 6-11.doi: 10.6040/j.issn.1671-9352.0.2015.150

幂级数弱McCoy环

李敏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:2015-04-07 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:liminyjs@163.com
作者简介:李敏(1987— ), 女, 硕士研究生, 研究方向为代数学及其应用. E-mail: liminyjs@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)

Power series weak McCoy rings

LI Min¹, 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:2015-04-07 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 引入了幂级数弱McCoy环的概念。证明了:(1)设{R_i|i∈I}是一族环,如果每一个R_i(i∈I)是幂级数弱McCoy环,则∏_i∈IR_i是幂级数弱McCoy环;(2)如果环R是一个诣零半交换环,则R［x］是幂级数弱McCoy环当且仅当R是幂级数弱McCoy环;(3)设环R是一个α-相容的诣零半交换环,则R［x;α］是幂级数弱McCoy环。

关键词: 幂级数, 幂级数McCoy环, 幂级数弱Armendariz环, 幂级数弱McCoy环, McCoy环

Abstract: The concept of a power series weak McCoy ring is introduced. It is shown that(1)if every R_i(i∈I) is a power series weak McCoy ring, then ∏_i∈IR_i is a power series weak McCoy ring;(2)If R is a nil-semicommutative ring, then R［x］ is a power series weak McCoy ring if and only if R is a power series weak McCoy ring;(3)If R is a α-compatible nil-semicommutative ring, then R［x;α］ is a power series weak McCoy ring.

Key words: power series weak McCoy ring, power series weak Armendariz ring, McCoy ring, power series McCoy ring, power series

中图分类号:

O153.3

李敏,王尧,任艳丽. 幂级数弱McCoy环[J]. 山东大学学报（理学版）, 2016, 51(2): 6-11.

LI Min, WANG Yao, REN Yan-li. Power series weak McCoy rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 6-11.

参考文献

[1] KIM N K, LEE K H, LEE Y. Power series rings satisfying a zero divisor property[J]. Comm Algebra, 2006, 34(6):2205-2218.
[2] HIZEM S. A note on nil power serieswise Armendariz rings[J]. Rend Circ Mat Palermo, 2010, 59(1):87-99.
[3] YANG Shizhou, SONG Xuemei, LIU Zhongkui. Power-serieswise McCoy rings[J]. Algebra Colloq, 2011, 18(2):301-310.
[4] HONG C Y, KIM N K, KWAK T K. Nilradicals of skew power series rings[J]. Bull Korean Math Soc, 2004, 41(3):507-519.
[5] HUH C, KIM C O, KIM E J, et al. Nilradicals of power series rings and nil power series rings[J]. J Korean Math Soc, 2005, 42(5):1003-1015.
[6] HUH C, KIM H K, LEE D S, et al. Prime radicals of formal power series rings[J]. Bull Korean Math Soc, 2001, 38(4):623-633.
[7] NASR-ISFAHANI A, MOUSSAVI A. On skew power serieswise Armendariz rings[J]. Comm Algebra, 2011, 39(9):3114-3132.
[8] YING Zhiling, CHEN Jianlong, LEI Zhen. Extensions of McCoy rings[J]. Northeast Math J, 2008, 24(1):85-94.
[9] MOHAMMADI R, MOUSSAVI A, ZAHIRI M. On nil-semicommutative rings[J]. Int Electron J Algebra, 2012, 11:20-37.
[10] ANNIN S. Associated primes over skew polynomial rings[J]. Comm Algebra, 2002, 30(5):2511-2528.
[11] OUYANG Lunqun, CHEN Huanyin. On weak symmetric rings[J]. Comm Algebra, 2010, 38(2):697-713.
[12] MOHAMMADI R, MOUSSAVI A, ZAHIRI M. Weak McCoy Ore extensions[J]. Intern Math Forum, 2011, 6(2):75-86.

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幂级数弱McCoy环

Power series weak McCoy rings

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