[1] Zhang Cuiping, Chen Jianlong,. Weak M-Armendariz rings [J]. Journal of Southeast University (English Edition), 2009, 25 (1): 142-146. [doi:10.3969/j.issn.1003-7985.2009.01.030]

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Weak M-Armendariz rings()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 1

Page:

142-146

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2009-03-30

Info

Title:

Weak M-Armendariz rings

Author(s):

Zhang Cuiping¹;  2;  Chen Jianlong¹

¹Department of Mathematics, Southeast University, Nanjing 210096, China
²Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Keywords:

semicommutative rings;  M-Armendariz rings;  weak Armendariz rings;  weak M-Armendariz rings

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2009.01.030

Abstract:

For a monoid M, this paper introduces the weak M-Armendariz rings which are a common generalization of the M-Armendariz rings and the weak Armendariz rings, and investigates their properties.Moreover, this paper proves that:a ring R is weak M-Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T_n(R)over R is weak M-Armendariz;if I is a semicommutative ideal of ring R such that R/I is weak M-Armendariz, then R is weak M-Armendariz, where M is a strictly totally ordered monoid;if a ring R is semicommutative and M-Armendariz, then R is weak M×N-Armendariz, where N is a strictly totally ordered monoid;a finitely generated Abelian group G is torsion-free if and only if there exists a ring R such that R is weak G-Armendariz.

References:

[1] Rege M B, Chhawchharia S.Armendariz rings [J].Proc Japan Acad Ser A Math Sci, 1997, 73(1):14-17.
[2] Armendariz E P.A note on extension of Bear and pp-rings [J].J Austral Math Soc, 1974, 18(2):470-473.
[3] Anderson D D, Camillo V.Armendariz rings and Gaussian rings [J].Comm Algebra, 1998, 26(7):2265-2272.
[4] Huh C, Lee Y, Smoktunowicz A.Armendariz rings and semicommutative rings [J].Comm Algebra, 2002, 30(2):751-761.
[5] Kim N K, Lee Y.Armendariz rings and reduced rings [J].J Algebra, 2000, 223(2):477-488.
[6] Liu Z K.Armendariz rings relative to a monoid [J].Comm Algebra, 2005, 33(3):649-661.
[7] Liu Z K, Zhao R Y.On weak Armendariz rings [J].Comm Algebra, 2006, 34(7):2607-2616.
[8] Ribenboim P.Noetherian rings of generalized power series [J].J Pure Appl Algebra, 1992, 79(3):293-312.

Memo

Memo:

Biographies: Zhang Cuiping(1974—), female, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10571026), the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20060286006).
Citation: Zhang Cuiping, Chen Jianlong.Weak M-Armendariz rings[J].Journal of Southeast University(English Edition), 2009, 25(1):142-146.

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