La dimensión debil de los anillos clásicos

Abstract

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