Some characterizations of regular modules.

Título inglés Some characterizations of regular modules.
Título español Caracterizaciones de módulos regulares.
Autor/es Azumaya, Goro
Organización Dep. Math. Univ. Indiana, Bloomington (Indiana), Estados Unidos
Revista 0214-1493
Publicación 1990, 34 (2): 241-248, 6 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120105
Palabras clave español Teoría de anillos ; Anillos ; Módulos
Icono pdf Acceso al artículo completo