Let Λ be a left and right Noetherian ring. For a positive integer k, we give an equivalent
condition that flat dimensions of the first k terms in the minimal injective resolution of Λ are …

It follows immediately from the proof of the existence of the injective hull E (M) of a module M
(see eg [1]) that an upper bound for the cardinality of E (M) is| M|| R|. On the other hand, over …

Bass characterized the rings R with the property that every left R-module has a projective
cover. These are the left perfect rings. A ring is left perfect if and only if the class of projective …

Let M be a finitely generated torsion-free module over a one-dimensional reduced
Noetherian ring R with finitely generated normalization. The rank of M is the tuple of vector …

The purpose of this paper is to study the structure of rings over which every essential
extension of a direct sum of a family of simple modules is a direct sum of automorphism …

Let R be a reduced one-dimensional Noetherian ring with finite integral closure R, and
conductor C and let@(A) denote the set of isomorphism classes of finitely generated …

Throughout this paper it is assumed that rings are associative, have the identity element,
and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R …

In an earlier paper C31, we introduced the concept of the Krull dimension of a right
Noetherian ring relative to a torsion theory and developed a method of evaluating it in …

Let A be a right order in a semisimple ring $\Sigma,{M_A} $ be a finite-dimensional
torsionless right A-module and ${\hat M_A} $ be the injective hull of M. JM Zelmanowitz has …