Let Rbe a ring with unity. A short exact sequence E of left R-modules is said to be neat-exact
if every simple left R-module is projective with respect to it. We call it P-pure-exact if for every …

Let R be a commutative ring with identity. A short exact sequence E of R-modules is said to
be neat (respectively, P-pure) if the sequence Hom R (S, E)(respectively, S⊗ RE) is exact for …

Following PM Cohn we calI a submodule P of the left A-module M pure iff 0--~ E~ P--~ E® M
is exact for aIl rte modules E. This generalizes the definition of purity for abelian groups, and …

We give a complete characterization of the class of commutative rings R possessing the
property that Spec (R) is weakly 0-dimensional. They turn out to be the same as strongly π …

We call a right module weakly neat-flat if is surjective for any epimorphism and any simple
right ideal. A left module is called weakly absolutely s-pure if is monic, for any …

Bazzoni and Salce have showed that all modules over a commutative domain R have a
strongly flat cover if and only if every flat R-module is strongly flat and that holds if and only if …

arXiv:1005.4168v1 [math.RA] 23 May 2010 Page 1 arXiv:1005.4168v1 [math.RA] 23 May
2010 RINGS WHOSE PROPER FACTORS ARE RIGHT PERFECT ALBERTO FACCHINI …

Let R be a commutative ring. It is known that any injective endomorphism of finitely
generated R-module is an isomorphism if and only if every prime ideal of R is maximal. This …

In this paper, we first introduce and study the notion of $\tau_q $-projective modules via
strongly Lucas modules, and then investigate the $\tau_q $-global dimension $\tau_q $-\gld …

PM Cohn [7] calls a submodule P of the left A-module M pure iff 0→ E⊗ P→ E⊗ M is exact for
all right modules E. This definition of purity, which Cohn [7] has shown to be equivalent to …