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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (5): 505-511    DOI: 10.3785/j.issn.1008-9497.2016.05.001
数学与计算机科学     
微分多项式环的半交换性和对称性
任艳丽1, 张玖琳2, 王尧2
1. 南京晓庄学院 数学与信息技术学院, 江苏 南京 211171;
2. 南京信息工程大学 数学与统计学院, 江苏 南京 210044
The semicommutativity and symmetry of differential polynomial rings
REN Yanli1, ZHANG Jiulin2, WANG Yao2
1. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China;
2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
 全文: PDF(626 KB)  
摘要： 研究微分多项式环R[x；δ]和Ore扩张环R[x；α，δ]的广义半交换性质和广义对称性质，使用逐项分析方法证明了：设R是δ-Armendariz环，则R[x；δ]是诣零半交换环（弱半交换环、广义弱对称环、弱zip环、右弱McCoy环）当且仅当R是诣零半交换环（弱半交换环、广义弱对称环、弱zip环、右弱McCoy环）；设R是弱2-素环和（α，δ）-条件环，则R[x；α，δ]是诣零半交换环（分别地，弱半交换环，广义弱对称环）.
关键词： 弱2-素环;  δ  -Armendariz环;  (α  δ  )-条件环;  诣零半交换环;  广义弱对称环    
Abstract: This paper investigates the generalized semicommutativity and generalized symmetry of the differential polynomial rings and Ore extensions of a ring. By using the itemized analysis method on polynomials, we proved that if R is δ-Armendariz ring, then R[x;δ] is nil-semicommutative ring (resp., weakly semicommutative, generalized weak symmetry (GWS), weak zip, right weak McCoy) if and only if R is nil-semicommutative ring (resp., weakly semicommutative, GWS, weak zip, right weak McCoy). Moreover, if R is a weakly 2-primal and (α,δ)-condition ring, then R[x;α,δ] is nil-semicommutative ring (resp., weakly semicommutative, GWS).
Key words: weakly 2-primal ring    δ-Armendariz ring    (α,δ)-condition ring    nil-semicommutative ring    generalized weak symmetry ring
收稿日期: 2015-11-20 出版日期: 2016-05-01
CLC:  O153.3  
基金资助: 国家自然科学基金资助项目（11071097）；江苏省自然科学基金资助项目（BK20141476）.
作者简介: 任艳丽(1965-),ORCID:http://orcid.org/0000-0002-2439-6172,女,硕士,教授,主要从事环论研究,E-mail:renyanlisx@163.com.
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引用本文:

任艳丽, 张玖琳, 王尧. 微分多项式环的半交换性和对称性[J]. 浙江大学学报（理学版）, 2016, 43(5): 505-511.

REN Yanli, ZHANG Jiulin, WANG Yao. The semicommutativity and symmetry of differential polynomial rings. Journal of Zhejiang University (Science Edition), 2016, 43(5): 505-511.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.001    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I5/505

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