On the weak McCoy property of skew inverse Laurent series rings

WANG Yao; SHI Yeping; REN Yanli

doi:10.13471/j.cnki.acta.snus.2020A020

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On the weak McCoy property of skew inverse Laurent series rings

Research articles | 更新时间：2023-11-01

- On the weak McCoy property of skew inverse Laurent series rings
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 5, Pages: 150-158(2022)
- 作者机构：
  
  1.南京信息工程大学数学与统计学院，江苏南京 210044
  2.南京晓庄学院信息工程学院，江苏南京 211171
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020A020
  CLC： O153.3
- Published：25 September 2022，
  
  Published Online：24 March 2022，
  
  Received：15 May 2020，
  
  Accepted：28 October 2021
扫描看全文
王尧,史叶萍,任艳丽.斜逆洛朗级数环的弱McCoy性[J].中山大学学报(自然科学版),2022,61(05):150-158.

WANG Yao,SHI Yeping,REN Yanli.On the weak McCoy property of skew inverse Laurent series rings[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):150-158.
王尧,史叶萍,任艳丽.斜逆洛朗级数环的弱McCoy性[J].中山大学学报(自然科学版),2022,61(05):150-158. DOI： 10.13471/j.cnki.acta.snus.2020A020.

WANG Yao,SHI Yeping,REN Yanli.On the weak McCoy property of skew inverse Laurent series rings[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):150-158. DOI： 10.13471/j.cnki.acta.snus.2020A020.

摘要

设

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447947&type=

2.79399991

2.37066650

是环

上的一个自同构，

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447984&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447965&type=

2.20133328

2.37066650

是

上的一个

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447988&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447986&type=

2.11666679

2.28600001

-导子，本文引进

</mo><mi>δ</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447994&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49447991&type=

7.61999989

2.96333337

-SILS右弱McCoy环的概念，采用分项讨论方法，给出该环的刻画，探讨它们的结构性质，丰富一般斜逆洛朗级数环的研究。

Abstract

Let

be a ring with an automorphism

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449585&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449584&type=

2.45533323

2.62466669

and a

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449589&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449588&type=

2.45533323

2.62466669

-derivation

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449587&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449586&type=

1.77800000

2.62466669

. We introduce the concept of

</mo><mi>δ</mi><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49448889&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49448888&type=

8.89000034

3.47133350

-SILS right weak McCoy rings，give their characterizations and investigate their structural properties by means of the itemized discussion method， enriching the research of general skew inverse Laurent series rings.

关键词

斜逆洛朗级数环右弱McCoy环环扩张

Keywords

skew inverse Laurent series ringright weak McCoy ringextension of rings

references

LETZTER E S，WANG L. Noetherian skew inverse power series rings ［J］. Algebras Represent Theory，2010，13（3）：303-314.

TUGANBAEV D A. Laurent series rings and pseudo-differential operator rings ［J］. J Math Sci，2005，128（3）：2843-2893.

ALHEVAZ A，KIANI D. On primeness of general skew inverse Laurent series ring ［J］. Commun Algebra，2017，45（3）：919-923.

HABIBI M，MOUSSAVI A，MOKHTARI S. On skew Armendariz of Laurent series type rings ［J］. Commun Algebra，2012，40（11）：3999-4018.

PAYKAN K，MOUSSAVI A. Study of skew inverse Laurent series rings ［J］. J Algebra Appl，2017，16（12）：1750221.

ALHEVAZ A，KIANI D. On zero-divisors in skew inverse Laurent series over noncommutative rings ［J］.Commun Algebra，2014，42（2）：469-487.

YANG S，SONG X，LIU Z. Power-serieswise McCoy rings ［J］. Algebra Colloq，2011，18（2）：301-310.

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.

ALHEVAZ A，KIANI D. Radicals of skew inverse Laurent series rings ［J］. Commun Algebra，2013，41（8）：2884-2902.

史叶萍，王尧，任艳丽. 斜逆 Laurent 级数环的弱 Armendariz 性质［J］. 吉林大学学报（理学版），2020，58（4）：808-814.

OUYANG L，LIU J. On weak <math id="M758"><mo stretchy="false">(</mo><mi>α</mi><mo>,</mo><mi>δ</mi><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449620&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49449610&type=7.281332972.96333337-compatible rings ［J］. Int J Algebra，2011，5（26）：1283-1296.

HWANG S U，JEON Y C，LEE Y. Structure and topological conditions of NI rings ［J］. J Algebra，2006，302（1）：186-199.

CHENG G. CHEN J. The structure of ring R［D，C］ and its characterizations ［J］. J Nanjing Univ Math Biquarterly，2007，24（1）：20-28.

CHEN J，YANG X，ZHOU Y. On strongly clean matrix and triangular matrix rings ［J］. Commun Algebra，2006，34（10）：3659-3674.

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