… More generally, a projective module has a semiperfect endomorphism ring if and only if it
is a finite direct sum of modules each of which has a local endomorphism ring. …

… It turns out that the structure of these modules can be described … of Bass, that a projective
module is semi-perfect if and only if … We define a perfect module as a projective module with the …

… called a projective module semiperfect if every homomorphic image has a projective cover
and … If M is a finitely generated projective module and end M is a semiregular ring, we do not …

… Observe that we did not show that the indecomposable projective modules over the ring R
of … that a ring is semiperfect if and only if each of its simple modules has a projective cover. A …

… exchange ring if and only if R/J(R) is an exchange ring and … semiperfect rings are exchange
rings or, in other words, that all finitely generated projective modules over a semiperfect ring …

… , we note that a projective semiregular module need not be F-semiperfect. Then, we …
projective module RM such that End(RM) is a semiregular ring but RM is not a semiregular module, …

… We now review some of useful properties of locally projective modules: … module is cyclic,
we know by Theorem 3 that the left R-module R is generalized semi-perfect if and only if the ring …

… If a ring R is a p-semiperfect ring for a normal preradical p, then we have p(R)=J(R) by (1.3)
and hence p(P)=J(P) for any projective module P. But this need not guarantee that p=J even …

… that a ring R is -semiperfect if and only if every finitely generated R-module has a projective
-… A projective τ-cover of M is a projective module P with an epimorphism f from P to M such …

… ring with identity is semiperfect if and only if every simple right module has a projective cover.
… to characterize right perfect rings as those for which every semisimple right module has a …