JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (12): 1-6.doi: 10.6040/j.issn.1671-9352.0.2015.629

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Quasi-linearly Armendariz modules

ZHANG Dong-qing, YIN Xiao-bin*, GAO Han-peng   

  1. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2015-12-29 Online:2016-12-20 Published:2016-12-20

Abstract: The quasi-linearly Armendariz modules which are a common generalization of linearly Armendariz modules and quasi-linearly Armendariz rings is introduced. Some basic properties of such modules are studied, some equivalent characteristics of quasi-linearly Armendariz modules are given, and the relationships between quasi-linearly Armendariz modules and the other modules are discussed.

Key words: Armendariz modules, quasi-Armendariz modules, linearly Armendariz modules, quasi-linearly Armendariz modules, quasi-Armendariz rings

CLC Number: 

  • O153.3
[1] REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Pro Japan Acad Ser A Math Sci, 1997, 73(1):14-17.
[2] ANDERSON D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998(26):2265-2272.
[3] KIM N K, LEE Y. Armendariz rings and reduced rings[J]. J Algebra, 2000, 223(2):477-488.
[4] ZHANG C P, CHEN J L. Quasi-Armendariz Modules[J]. J Math Res Exposition, 2010(30):734-742.
[5] LEE T K, WONG T L. On weak Armenndariz rings[J]. Houston J Math, 2003(29):583-593.
[6] JEON Y C, KIM H K, LEE, et al. On weak-Armendariz rings[J]. Bull Korean Math Soc, 2009(46):135-146.
[7] HIRANO Y. On annihilator ideals of a polynomial ring over a noncommutative ring[J]. J Pure Appl Algebra, 2002, 168(1):45-52.
[8] 佟文廷. 同调代数引论[M]. 北京: 高等教育出版社, 1998.
[9] KIM N K, LEE. Armendariz rings and reduced rings[J]. J Algebra, 2000, 223:477-488.
[10] REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Pro Japan Acad Ser A Math Sci, 1997, 73(1):14-17.
[11] CUI J, XHEN Jianlong. On McCoy modules[J]. Bull Koren Math Soc, 2011(48):23-33.
[12] STENSTROM B. Ring of Quotients[M]. New York: Springer-Verlag, 1975.
[13] ARMENDARIZ E P. A note on extensions of Bear and P.P.-rings[J]. J Austral Math Soc, 1974, 18:470-473.
[14] ARMENDARIZ D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998, 26(7):2265-2272.
[15] HIRANO Y. On annihilator ideals of a polynomial ring over a noncommutative ring[J]. J Pure Appl Algebra, 2002, 168(1):45-52.
[1] 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.
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