La dimensión debil de los anillos clásicos
- 1 Universidad de Murcia. Departamento de Álgebra y Fundamentos
ISSN: 0214-1493
Ano de publicación: 1980
Número: 20
Páxinas: 141-144
Tipo: Artigo
Outras publicacións en: Publicacions matematiques
Resumo
"The weak dimension of a ring R, wD(R), is shown to be equal to the supremum of the injective dimensions of the pure-injective left R-modules . Using this result and the structure theorem for pure-injectives over commutative rings ([2]), the weak . dimension of a (commutative) classical ring ([91) is characterized as the supremum of the injective dimensions of the cocyclic modules . Characterizations of the classical rings R for which wD(R),<1 are given and it is also shown that, for certain classical rings R, wD(R) is the supremum of the injective dimensions of the simple modules. "