… 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 …

… , 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 …

… projective module P is a projective cover of M if there is an epimorphism ~ : P ~ M such that
Ker is small in P. An injective module … A ring is semi-perfect if every finitely generated module …

… every projective module is a direct s free module, we may assume that P is a free module, …
Since every projective module is a direct summand of a free module, we may assume that P …

… 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 …

… is free, generalizes to semiperfect rings as follows" … Every projective module over a semi-perfect
ring is the direct sum … of those rings for which every simple right-module has a projective …

… call a left R-module P an F-semi-perfect module if B is projective and if, for … projective modules
in general. In fact, we can see that if a free left module with an infinite free basis over a ring …