约化环上矩阵环的一类拟Armendariz子环

doi:10.6040/j.issn.1671-9352.0.2014.310

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (04): 67-70.doi: 10.6040/j.issn.1671-9352.0.2014.310

约化环上矩阵环的一类拟Armendariz子环

张万儒, 郭金生

河西学院数学与统计学院, 甘肃张掖 734000

收稿日期:2014-07-04 修回日期:2014-11-11 出版日期:2015-04-20 发布日期:2015-04-17
通讯作者: 郭金生(1979-),男,硕士,讲师,研究方向为生物数学.E-mail:guojinsheng1979@163.com E-mail:guojinsheng1979@163.com
作者简介:张万儒(1980-),男,硕士,讲师,研究方向为环理论.E-mail:zhangwru@163.com
基金资助:
河西学院青年教师科研基金(QN2012-14)

A class of quasi-Armendariz subrings of matrix rings over reduced rings

ZHANG Wan-ru, GUO Jin-sheng

School of Mathematics and Statistics, Hexi University, Zhangye 734000, Gansu, China

Received:2014-07-04 Revised:2014-11-11 Online:2015-04-20 Published:2015-04-17

摘要/Abstract

摘要： 讨论了reduced环上n阶矩阵环M_n(R)的一类特殊拟Armendariz子环S_n(R).证明了如果R是reduced环,α₂,…,α_n是R的相容自同态,那么S_n(R)是拟Armendariz环.

关键词: reduced环, 相容自同态, 拟Armendariz环

Abstract: A class of special quasi-Armendariz subrings S_n(R) of the n×n matrix ring M_n(R) over a reduced ring is investigated. It is shown that S_n(R) is a quasi-Armendariz ring if R is a reduced ring with compatible endomorphisms α₂,…,α_n.

Key words: quasi-Armendariz rings, compatible endomorphism, reduced rings

中图分类号:

O153.3

张万儒, 郭金生. 约化环上矩阵环的一类拟Armendariz子环[J]. 山东大学学报（理学版）, 2015, 50(04): 67-70.

ZHANG Wan-ru, GUO Jin-sheng. A class of quasi-Armendariz subrings of matrix rings over reduced rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 67-70.

参考文献

[1] REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Proc Japan Acad: Ser A, 1997, 73(1):14-17.
[2] ANDERSON D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998, 26(7):2265-2272.
[3] LEE T K, ZHOU Y. Armendariz and reduced rings[J]. Comm Algebra, 2004, 32(6):2287-2299.
[4] KWAK T K, LEE Y, YUN S J. The Armendariz property on ideals[J]. J Algebra, 2012, 354:121-135.
[5] ANTOINE R. Examples of Armendariz rings[J]. Comm Algebra, 2002, 38(11):4130-4143.
[6] NASR-ISFAHANI A R. Radicals of skew polynomial and skew laurent polynomial rings over skew Armendariz rings[J]. Comm Algebra, 2014, 42(3):1337-1349.
[7] HIRANO Y. On annihilator ideals of a polynomial ring over a noncommutative ring[J]. J Pure Appl Algebra, 2002, 168:45-52.
[8] HASHEMI E. Quasi-Armendariz rings relative to a monoid[J]. J Pure Appl Algebra, 2007, 211:374-382.
[9] BASER M, KAYNARCA F, KWAK T K, et al. Weak quasi-Armendariz rings[J]. Algebra Colloq, 2011, 18(4):541-552.
[10] ANNIN S. Associated primes over skew polynomial rings[J]. Comm Algebra, 2002, 30(5):2511-2528.
[11] LIU Zhongkui, QIAO Husheng. Generalized pp and zip subrings of matrix rings[J]. Communications in Mathematical Research, 2010, 26(3):193-202.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

约化环上矩阵环的一类拟Armendariz子环

A class of quasi-Armendariz subrings of matrix rings over reduced rings

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

多维度评价

本文评价

推荐阅读 0

[1]	丁婷婷,吴俊,张培雨. 弱σ-斜拟Armendariz环[J]. 山东大学学报（理学版）, 2014, 49(2): 7-11.
[2]	马晶, 郭颖, 孙成侠. 一类半交换的Armendariz环[J]. 山东大学学报（理学版）, 2014, 49(10): 1-6.
[3]	王文康 . 一类上三角矩阵环的Armendariz与半交换性质[J]. J4, 2008, 43(2): 62-65 .
[4]	王文康 . 矩阵环的极大的广义Armendariz子环[J]. J4, 2007, 42(8): 74-78 .