A bstract This thesis is essentially an exposition of the standard resu1ts on perfect and semi-
perfect rings. Complete characterizations of perfect and sen" li-perfect rings are given in …

PROOF. Let S be a simple right R/J module, then S is a simple right R-module, hence has an
R-projective cover. By [1, Lemma 2.2], S has an R/J projective cover. Since S was arbitrary, it …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

Pseudo-Semisimple Rings Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 85, Number 2, June 1982 PSEUDO-SEMISIMPLE RINGS SAAD MOHAMED …

Semi-perfect and perfect modules were introduced by Mares [3] as generalizations of
Bass'[2] notions of semi-perfect and perfect rings. She developed a substantial structure …

The pioneering work on perfect rings was clone by Bass [3] ard most of the principal
characterizations of lcft perfect rings are contained in [3, Theorem PI.(See Anderson and …

Introduction. In this paper we give a characterization of semiperfect rings with projective,
essential left socle (Theorems 5.1 and 4.4). This characterization is effected through the use …

In the seminal paper [1], Bass provided a number of characterizations of left perfect rings. In
the course of the proof of his" Theorem P", Bass implicitly showed that the ring R is left …

We say that a subring R0 of a ring R is semi-invariant if R0 is the ring of invariants in R under
some set of ring endomorphisms of some ring containing R. We show that R0 is semi …

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