It is known that every complex of left R-modules has an exact cover. We consider the
question of finding R for which every complex of left i?-modules has an exact envelope. We …

A ring R is left noetherian if and only if the direct sum of injective envelopes of any family of
left R-modules is the injective envelope of the direct sum of the given family of modules (or …

In [2, page 151], J. Lambek proposes the following exercise: With any maximal right ideal M
of a ring R with 1 associate the ideal. Show that OM, is the right annihilator of the injective …

A CHARACTERIZATION OF LEFT PERFECT RINGS Page 1 Canad. Math. Bull. Vol. 38 (3),
1995 pp. 382-384 A CHARACTERIZATION OF LEFT PERFECT RINGS YIQIANG ZHOU …

We prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

It is shown that every pure-injective right module over a ring R is a direct sum of lifting
modules if and only if R is a ring of finite representation type and right local type. In …

In this note, we study rings over which every left module is a direct sum of finitely generated
modules. Chase [5] showed that all such rings are left artinian and Fuller [8] proved that …

This peper 142s motivated by one of Dinh van Huynh and. PF Sn? ith [a] in which some new
characterizations of semiprime Artinian rings and left Xoetherian rings were given by their c …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

The notion of generalized projective covers Is Introduced to give a natural generalization of
a theorem of Bass on perfect rings. Moreover, In terms of this notion, some characterizations …