Some characterizations of regular modules

• Autores: Goro Azumaya
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 34, Nº 2, 1990, págs. 241-248
• Idioma: inglés
• Títulos paralelos:
  • Caracterizaciones de módulos regulares
• Enlaces
  • Texto completo
• Resumen

  • Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x Î M there exists a homomorphism F: M ? R such that f(x) = x. Let Q be a left R-module and h: Q ? M a homomorphism. We call h locally split if for every x Î M there exists a homomorphism g: M ? Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:

    (1) M is Zelmanowitz-regular.

    (2) every homomorphism into M is locally split.

    (3) M is locally projective and every cyclic submodule of M is a direct summand of M.