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[1] Cui Jian, Chen Jianlong,. Uniquely strongly clean triangular matrix rings [J]. Journal of Southeast University (English Edition), 2011, 27 (4): 463-465. [doi:10.3969/j.issn.1003-7985.2011.04.023]
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Uniquely strongly clean triangular matrix rings()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
27
Issue:
2011 4
Page:
463-465
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2011-12-31

Info

Title:
Uniquely strongly clean triangular matrix rings
Author(s):
Cui Jian;  Chen Jianlong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
uniquely strongly clean ring;  uniquely bleached local ring;  triangular matrix ring
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2011.04.023
Abstract:
An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n×n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J(R)≅Z2.

References:

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Memo

Memo:
Biographies: Cui Jian(1984—), male, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10971024), the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024), the Natural Science Foundation of Jiangsu Province(No.BK2010393).
Citation: Cui Jian, Chen Jianlong.Uniquely strongly clean triangular matrix rings[J].Journal of Southeast University(English Edition), 2011, 27(4):463-465.[doi:10.3969/j.issn.1003-7985.2011.04.023]
Last Update: 2011-12-20