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| 微分多项式环的半交换性和对称性 | |
| 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. |
| 作者姓名： | 任艳丽 张玖琳 王尧 |
| 作者单位： | 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 |
| 基金项目： | 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）. |
| 摘 要： | 研究微分多项式环Rx；δ]和Ore扩张环Rx；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Rx；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Rx；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 &delta -Armendariz环 (&alpha &delta )-条件环 诣零半交换环 广义弱对称环 |
| 收稿时间： | 2015-11-20 |
The semicommutativity and symmetry of differential polynomial rings |
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| REN Yanli,ZHANG Jiulin,WANG Yao.The semicommutativity and symmetry of differential polynomial rings[J].Journal of Zhejiang University(Sciences Edition),2016,43(5):505-511. | |
| Authors: | REN Yanli ZHANG Jiulin WANG Yao |
| Institution: | 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 |
| 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 Rx;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 Rx;α,δ] is nil-semicommutative ring (resp., weakly semicommutative, GWS). |
| Keywords: | weakly 2-primal ring δ-Armendariz ring (α δ)-condition ring nil-semicommutative ring generalized weak symmetry ring |
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