[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2007.44.4.903

WEAKLY STABLE CONDITIONS FOR EXCHANGE RINGS

Chen, Huanyin (DEPARTMENT OF MATHEMATICS HUNAN NORMAL UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 903-913 More about this Journal

Abstract

A ring R has weakly stable range one provided that aR+bR=R implies that there exists a $y{\in}R$ such that $a+by{\in}R$ is right or left invertible. We prove, in this paper, that every regular element in an exchange ring having weakly stable range one is the sum of an idempotent and a weak unit. This generalize the corresponding result of one-sided unit-regular ring. Extensions of power comparability and power cancellation are also studied.

Keywords

exchange rings; weakly stable range one; power comparability; power cancellation;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
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Reference

1	T. Wu, The power-substitution condition of endomorphism rings of quasi-projective modules, Comm. Algebra 28 (2000), no. 1, 407-418 DOI ScienceOn
2	K. R. Goodearl, von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979; second ed., Krieger, Malabar, Fl., 1991
3	Q. Li, J. Zhu, and W. Tong, On related power comparability of modules, Comm. Algebra 31 (2003), no. 10, 4925-4938 DOI ScienceOn
4	H. Chen, Exchange rings with artinian primitive factors, Algebr. Represent Theory 2 (1999), no. 2, 201-207 DOI
5	V. P. Camillo and D. Khurana, A characterization of unit regular rings, Comm. Algebra 29 (2001), no. 5, 2293-2295 DOI ScienceOn
6	H. Chen, Elements in one-sided unit regular rings, Comm. Algebra 25 (1997), no. 8, 2517-2529 DOI ScienceOn
7	H. Chen, Comparability of modules over regular rings, Comm. Algebra 25 (1997), no. 11, 3531-3543 DOI ScienceOn
8	H. Chen, Power-substitution, exchange rings and unit ${\pi}-regularity$ , Comm. Algebra 28 (2000), no. 11, 5223-5233 DOI ScienceOn
9	H. Chen, Exchange rings satisfying power ideal-cancellation, Sci. China Ser. A 46 (2003), no. 6, 804-814 DOI
10	Q. Li and W. Tong, Weak cancellation of modules and weakly stable range conditions for exchange rings, Acta Math. Sinica (Chinese) 45 (2002), no. 6, 1121-1126
11	A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002
12	J. Wei, Exchange rings with weakly stable range one, Vietnam J. Math. 32 (2004), no. 4, 441-449
13	T. Wu, The problem of weak cancellation of modules and qu-regular rings, Acta Math. Sinica (Chinese), 38 (1995), no. 6, 746-751
14	J. Wei, Unit-regularity and stable range conditions, Comm. Algebra 33 (2005), no. 6, 1937-1946 DOI ScienceOn