JOURNAL BROWSE
Search
Advanced SearchSearch Tips
EXTENSIONS OF GENERALIZED STABLE RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
EXTENSIONS OF GENERALIZED STABLE RINGS
Wanru, Zhang;
  PDF(new window)
 Abstract
In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e, . . . , e} of idempotents such that eRe, . . . , eRe are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.
 Keywords
generalized stable rings;complete orthogonal set of idempotents;ring extensions;
 Language
English
 Cited by
1.
Stable range and almost stable range, Journal of Pure and Applied Algebra, 2012, 216, 10, 2094  crossref(new windwow)
 References
1.
P. Ara, G. K. Pedersen, and F. Perera, An infinite analogue of rings with stable rank one, J. Algebra 230 (2000), no. 2, 608-655 crossref(new window)

2.
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), no. 1, 25-42 crossref(new window)

3.
H. Y. Chen, Full elements in one-sided unit-regular rings, Comm. Algebra 33 (2005), no. 11, 4115-4123 crossref(new window)

4.
H. Y. Chen, Full elements in regular rings, Taiwanese J. Math. 8 (2004), no. 2, 203-209 crossref(new window)

5.
H. Y. Chen, Generalized stable exchange rings, Algebra Colloq. 15 (2008), no. 2, 193-198 crossref(new window)

6.
H. Y. Chen, Generalized stable regular rings, Comm. Algebra 31 (2003), no. 10, 4899-4910 crossref(new window)

7.
H. Y. Chen, On exchange $QB_{\infty}-rings, Algebra Colloq. 14 (2007), no. 4, 613-623 crossref(new window)

8.
H. Y. Chen, On exchange QB-rings, Comm. Algebra 31 (2003), no. 2, 831-841 crossref(new window)

9.
H. Y. Chen, On generalized stable rings, Comm. Algebra 28 (2000), no. 4, 1907-1917 crossref(new window)

10.
H. Y. Chen, On QB endomorphism rings, Comm. Algebra 35 (2007), no. 12, 4005-4017 crossref(new window)

11.
H. Y. Chen, On $QB_{\infty}-rings$, Comm. Algebra 34 (2006), no. 6, 2057-2068 crossref(new window)

12.
W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278 crossref(new window)

13.
W. K. Nicholosn, J. K. Park, and M. F. Yousif, Extensions of simple-injective rings, Comm. Algebra 28 (2000), no. 10, 4665-4675 crossref(new window)

14.
J. Q. Wei, Unit-regularity and stable range conditions, Comm. Algebra 33 (2005), no. 6, 1937-1946 crossref(new window)