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[1] Wang Zhou, Chen Jianlong,. Extensions of strongly π-regular general rings [J]. Journal of Southeast University (English Edition), 2007, 23 (2): 309-312. [doi:10.3969/j.issn.1003-7985.2007.02.031]
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Extensions of strongly π-regular general rings()
强 π-正则一般环的扩张
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
23
Issue:
2007 2
Page:
309-312
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2007-06-30

Info

Title:
Extensions of strongly π-regular general rings
强 π-正则一般环的扩张
Author(s):
Wang Zhou;  Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 210096, China
王周;  陈建龙
东南大学数学系, 南京 210096
Keywords:
strongly π-regular general ring;  strongly clean general ring;  upper triangular matrix general ring;  trivial extension
强π-正则一般环;  强clean一般环;  上三角矩阵一般环;  平凡扩张
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2007.02.031
Abstract:
The concept of the strongly π-regular general ring(with or without unity)is introduced and some extensions of strongly π-regular general rings are considered.Two equivalent characterizations on strongly π-regular general rings are provided.It is shown that I is strongly π-regular if and only if, for each x∈I, xn=xn+1y=zxn+1 11for n≥1 and y, z∈I if and only if every element of I is strongly π-regular.It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
介绍了强π-正则一般环(未必有单位元)的概念并考虑了它的一些扩张.给出了强π-正则一般环的2个等价刻画, 即I是强π-正则一般环当且仅当对于每个x∈I, 存在n≥1以及y, z∈I, 使得xn=xn+1y=zxn+111当且仅当I中的每个元都是强π-正则的.还考虑了强π-正则一般环上的上三角矩阵一般环和平凡扩张, 证明了强π-正则一般环上的上三角矩阵一般环仍是强π-正则的并且其平凡扩张是强clean的.

References:

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Memo

Memo:
Biographies: Wang Zhou(1979—), male, graduate;Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Last Update: 2007-06-20