DOI QR코드

DOI QR Code

EXTENSIONS OF GENERALIZED STABLE RINGS

  • Published : 2009.11.30

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$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ 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.

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 https://doi.org/10.1006/jabr.2000.8330
  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 https://doi.org/10.1016/S0022-4049(00)00055-4
  3. H. Y. Chen, Full elements in one-sided unit-regular rings, Comm. Algebra 33 (2005), no. 11, 4115-4123 https://doi.org/10.1080/00927870500261421
  4. H. Y. Chen, Full elements in regular rings, Taiwanese J. Math. 8 (2004), no. 2, 203-209 https://doi.org/10.11650/twjm/1500407622
  5. H. Y. Chen, Generalized stable exchange rings, Algebra Colloq. 15 (2008), no. 2, 193-198 https://doi.org/10.1142/S1005386708000199
  6. H. Y. Chen, Generalized stable regular rings, Comm. Algebra 31 (2003), no. 10, 4899-4910 https://doi.org/10.1081/AGB-120023138
  7. H. Y. Chen, On exchange $QB_{\infty}-rings, Algebra Colloq. 14 (2007), no. 4, 613-623 https://doi.org/10.1142/S1005386707000569
  8. H. Y. Chen, On exchange QB-rings, Comm. Algebra 31 (2003), no. 2, 831-841 https://doi.org/10.1081/AGB-120017345
  9. H. Y. Chen, On generalized stable rings, Comm. Algebra 28 (2000), no. 4, 1907-1917 https://doi.org/10.1080/00927870008826935
  10. H. Y. Chen, On QB endomorphism rings, Comm. Algebra 35 (2007), no. 12, 4005-4017 https://doi.org/10.1080/00927870701509560
  11. H. Y. Chen, On $QB_{\infty}-rings$, Comm. Algebra 34 (2006), no. 6, 2057-2068 https://doi.org/10.1080/00927870600549550
  12. W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269-278 https://doi.org/10.2307/1998510
  13. W. K. Nicholosn, J. K. Park, and M. F. Yousif, Extensions of simple-injective rings, Comm. Algebra 28 (2000), no. 10, 4665-4675 https://doi.org/10.1080/00927870008827111
  14. J. Q. Wei, Unit-regularity and stable range conditions, Comm. Algebra 33 (2005), no. 6, 1937-1946 https://doi.org/10.1081/AGB-200063337

Cited by

  1. Stable range and almost stable range vol.216, pp.10, 2012, https://doi.org/10.1016/j.jpaa.2012.01.018