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[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()
弱 M-Armendariz 环
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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
弱 M-Armendariz 环
Author(s):
Zhang Cuiping1;  2;  Chen Jianlong1
1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
张翠萍1;  2;  陈建龙1
1东南大学数学系, 南京 210096; 2西北师范大学数学系, 兰州 730070
Keywords:
semicommutative rings;  M-Armendariz rings;  weak Armendariz rings;  weak M-Armendariz rings
半交换环;  M-Armendariz环;  弱Armendariz环;  弱M-Armendariz环
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 Tn(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.
对于幺半群M, 引入了弱M-Armendariz环的概念, 此概念是M-Armendariz环和弱 Armendariz环的共同推广.研究了这类环的性质, 并且证明了:R是弱M-Armendariz环当且仅当对任意的n, R的n阶上三角矩阵环Tn(R)是弱M-Armendariz环;如果I是环R的半交换理想, 使得R/I是弱M-Armendariz环, 则R是弱M-Armendariz环, 其中M是严格全序幺半群;如果R是半交换的M-Armendariz环, 则R是弱M×N-Armendariz环, 其中N是严格全序幺半群;有限生成Abelian群G是torsion-free的当且仅当存在一个环R, 使得R是弱G-Armendariz环.

References:

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[3] Anderson D D, Camillo V.Armendariz rings and Gaussian rings [J].Comm Algebra, 1998, 26(7):2265-2272.
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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.
Last Update: 2009-03-20