华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 3: 67 - 79

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.03.009

应用数学与基础数学

中心 McCoy 环

  • 王文康
展开
  • 西北民族大学 数学与计算机科学学院, 兰州 730124
王文康, 女, 教授, 研究方向为代数学

收稿日期: 2014-04-17

  网络出版日期: 2015-05-28

收起

Central McCoy rings

  • WANG Wen-Kang
Expand

Received date: 2014-04-17

  Online published: 2015-05-28

Fold

摘要

给出了中心McCoy环的性质. 证明了:
环R是中心McCoy环当且仅当R是中心McCoy环当且仅当R[x是中心McCoy环. 设R 是右Ore环, Q是它的右商环,如果R是中心McCoy环, 那么Q是中心McCoy环.

关键词： McCoy环中心McCoy环; 中心环;上三角矩阵环

本文引用格式

王文康 . 中心 McCoy 环[J]. 华东师范大学学报（自然科学版）, 2015 , 2015(3) : 67 -79 . DOI: 10.3969/j.issn.1000-5641.2015.03.009

Abstract

Central McCoy rings are a generalization of McCoy rings,and its properties were investigated. We showed that a ring R is central McCoy if and only if R[x] is central McCoy, and if and only if R[x] is central McCoy, where (xn) is theideal generated by xn and n is a positive integer. We get that for a right Ore ring R with Q its classical right quotient ring, if R is central McCoy, then Q is also centralMcCoy.

Key words： McCoy ring; central McCoy ring; central Armendarizring;upper triangular matrix ring

参考文献

[1]ARMENDARIZ E P. A note on extensions of Baer and p. p. rings [J].Aust Math Soc, 1974, 18: 470-473.
[2]REGE M B, CHHAWCHHARIA S. Armendariz rings [J]. Proc Japan Acad SerA, 1997, 73: 14-17.
[3]NAZIM A, GONCA G, ABDULLAH H, et al. Central Armendariz rings [J].Bull Malays Math Sci Soc, 2011, 34(1): 137-145.
[4]NIELSEN P P. Semi-commutativity and the McCoy condition [J]. JAlgebra, 2006, 298: 134-141.
[5]MCCOY N H. Remaks on divisors of zero [J]. Amer Math Monthly, 1942,49: 286-295.
[6]VICTOR C, NIELSEN P P. McCoy rings and zero-divisors [J]. Journal of Pure and Applied Algebra, 2008, 212: 599-615.
[7]CHAN Y H, YOUNG C J, KIM N K, et al. The McCoy condition on noncommutative rings [J]. Comm Algebra, 2011, 39: 1809-1825.
[8]KIM N K, LEE K H, LEE Y. Power series rings satisfying a zero divisor property [J]. Comm Algebra, 2006, 34: 2205-2218.
[9}YANG S Z, SONG X M, LIU Z K. Power-serieswise McCoy rings [J].Algebra Collquium, 2011, 18(2): 301-310.
[10]CHAN H, YANG L, AGATA S. Armendariz  rings and semicommutative rings[J]. Comm Algebra, 2002, 30: 751-761.
[11]LEI Z, CHEN J L, YING Z L. A question on McCoy rings [J]. Bull Austral Math Soc, 2007, 76: 137-141.
[12]YING Z L, CHEN J L, LEI Z. Extensions of McCoy rings [J].Northeasters mathematics journal, 2008, 24(1): 85-94.
[13]TUGANBAEV A A. Rings Close to Regular [M]. Dordrecht: Kluwer Academic Publishers, 2002.
[14]KIM N K, LEE Y. Extensions of reverdible rings [J]. J Pure Appl Algebra, 2003, 185: 207-223.
[15]ZHAO R Y, LIU Z K. Extensions of McCoy rings [J]. Algebra Collquium,2009, 16(3): 495-502.
[16]ANDERSON D D, CAMILLO. Armendariz rings and Gaussian rings [J]. Comm Algebra, 1998, 26: 2265-2272.
[17]MCCONNELL J C, ROBSON L C. Noncommutative Noetherian Rings [M].Chichester: John Wiley and Sons, 1987.
Options
文章导航

/

〈 〉