JOURNAL BROWSE
Search
Advanced SearchSearch Tips
WEAKLY STABLE CONDITIONS FOR EXCHANGE RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
WEAKLY STABLE CONDITIONS FOR EXCHANGE RINGS
Chen, Huanyin;
  PDF(new window)
 Abstract
A ring R has weakly stable range one provided that aR+bR=R implies that there exists a such that 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;
 Language
English
 Cited by
 References
1.
V. P. Camillo and D. Khurana, A characterization of unit regular rings, Comm. Algebra 29 (2001), no. 5, 2293-2295 crossref(new window)

2.
H. Chen, Elements in one-sided unit regular rings, Comm. Algebra 25 (1997), no. 8, 2517-2529 crossref(new window)

3.
H. Chen, Comparability of modules over regular rings, Comm. Algebra 25 (1997), no. 11, 3531-3543 crossref(new window)

4.
H. Chen, Exchange rings with artinian primitive factors, Algebr. Represent Theory 2 (1999), no. 2, 201-207 crossref(new window)

5.
H. Chen, Power-substitution, exchange rings and unit ${\pi}-regularity$, Comm. Algebra 28 (2000), no. 11, 5223-5233 crossref(new window)

6.
H. Chen, Exchange rings satisfying power ideal-cancellation, Sci. China Ser. A 46 (2003), no. 6, 804-814 crossref(new window)

7.
K. R. Goodearl, von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979; second ed., Krieger, Malabar, Fl., 1991

8.
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

9.
Q. Li, J. Zhu, and W. Tong, On related power comparability of modules, Comm. Algebra 31 (2003), no. 10, 4925-4938 crossref(new window)

10.
A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002

11.
J. Wei, Exchange rings with weakly stable range one, Vietnam J. Math. 32 (2004), no. 4, 441-449

12.
J. Wei, Unit-regularity and stable range conditions, Comm. Algebra 33 (2005), no. 6, 1937-1946 crossref(new window)

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.
T. Wu, The power-substitution condition of endomorphism rings of quasi-projective modules, Comm. Algebra 28 (2000), no. 1, 407-418 crossref(new window)