Exchange rings satisfying the related comparability

• Autores: Chen Huanyin, Li Fu-an
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 53, Fasc. 2, 2002, págs. 157-164
• Idioma: inglés
• Títulos paralelos:
  • Anillos de intercambio que satisfacen la comparabilidad relacionada
• Enlaces
  • Texto completo
• Resumen

  • In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.

• Referencias bibliográficas
  • P. Ara, Extensions of exchange rings, J. Algebra 197 (1997), 409–423.
  • P. Ara, Stability properties of exchange rings, International Symposium on Ring Theory (Proc. China-Korea-Japan Ring Theory Conference), 23–42,...
  • P. Ara, K.R. Goodearl, K.C. O’Meara, and E. Pardo, Separative cancellation for projective modules over exchange rings, Israel J. Math. 105...
  • P. Ara and E. Pardo, Refinement monoids with weak comparability and applications to regular rings and $C^\*$-algebras, Proc. Amer. Math. Soc....
  • V.P. Camillo and H.P. Yu, Stable range one for rings with many idempotents, Trans. Amer. Math. Soc. 347 (1995), 3141–3147.
  • H. Chen, Related comparability over regular rings, Algebra Colloq. 3 (1996), 277–282.
  • H. Chen, Elements in one-sided unit regular rings, Comm. Algebra 25 (1997), 2517–2529.
  • H. Chen, Comparability of modules over regular rings, Comm. Algebra 25 (1997), 3531–3543.
  • H. Chen, On related unit-regular elements, Algebra Colloq. 4 (1997), 323–328.
  • H. Chen, Exchange rings, related comparability and power-substitution, Comm. Algebra 26 (1998), 3383–3401.
  • H. Chen, Related comparability over exchange rings, Comm. Algebra 27 (1999), 4209–4216.
  • H. Chen, Elements in exchange rings with related comparability, Int. J. Math. Math. Sci. 23 (2000), 639–644.
  • M. Company Cabezos, M. Gómez Lozano, and M. Siles Molina, Exchange Morita rings, Comm. Algebra 29 (2001), 907–925.
  • K.R. Goodearl, Von Neumann regular rings, Pitman, London-San Francisco-Melbourne, 1979; 2nd ed., Krieger, Malabar, FL, 1991.
  • R.E. Hartwig and J. Luh, A note on the group structure of unit regular ring elements, Pacific J. Math. 71 (1977), 449–461.
  • W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269–278.
  • E. Pardo, Comparability, separativity, and exchange rings, Comm. Algebra 24 (1996), 2915–2929.
  • T.R. Savage, Generalized inverses in regular rings, Pacific J. Math. 37 (1980), 455–466.