In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

Let $ C $ be a semidualizing module over a commutative Noetherian local ring $ R $. In this
paper we introduce a new class of modules, namely $ C $-canonical modules which are a …

Given two rings A and R, we study the equivalences between all projective right A-modules
and all injective right R-modules. We prove that such equivalences exist if and only if AA and …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y-
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,
n)-injective if for any (m, n)-presented right R-module P; M is called (m, n)-flat if for any (m, n) …

Throughout, R is an associative ring with identity and all modules are unitary. Unless
otherwise specified, s is a class of some right R-modules which is closed under …

Let R be a ring and be a class of right R-modules which is closed under submodules,
quotients and isomorphisms. A right R-module M is called-injective if for every T. A ring R is …

Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, by using
the classes 𝒫 C and ℐ C, we extend the notions of perfect and coperfect modules introduced …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

Let R be an associative ring with identity. For a given class 𝒮 of finitely presented left
(respectively right) R-modules containing R, we present a complete characterization of 𝒮 …