|Table of Contents|

[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]
Copy

Extensions of strongly π-regular general rings()
Share:

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
Author(s):
Wang Zhou Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 210096, China
Keywords:
strongly π-regular general ring strongly clean general ring upper triangular matrix general ring trivial extension
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.

References:

[1] Dischinger M F.Sur les anneaux fortement π-réguliers [J].C R Acad Sci Paris: Series A, 1976, 283:571-573.
[2] Nicholson W K.Strongly clean rings and Fitting’s Lemma [J].Comm Algebra, 1999, 27(8):3583-3592.
[3] Ara P.Extensions of exchange rings [J].J Algebra, 1997, 197(2):409-423.
[4] Chen H Y, Chen M S.On strongly π-regular ideals [J].J Pure Appl Algebra, 2005, 195(1):21-32.
[5] Nicholson W K, Zhou Y Q.Clean general rings [J].J Algebra, 2005, 291(1):279-311.
[6] Ara P.Strongly π-regular rings have stable range one [J].Proc Amer Math Soc, 1996, 124(11):3293-3298.
[7] Anderson D D, Camillo V P.Commutative rings whose elements are a sum of a unit and an idempotent [J].Comm Algebra, 2002, 30(7):3327-3336.
[8] Chen J L, Zhou Y Q.Strongly clean power series rings [J].Proc Edinburgh Math Soc, 2007, 50(1):73-85.
[9] Nicholson W K. Lifting idempotents and exchange rings [J].Trans Amer Math Soc, 1977, 229:269-278.
[10] Nicholson W K, Zhou Y Q.Rings in which elements are uniquely the sum of an idempotent and a unit [J].Glasgow Math J, 2004, 46(2):227-236.

Memo

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