Because traditional ring theory places restrictive hypotheses on all submodules of a module,
its results apply only to small classes of already well understood examples. Often, modules …

Let R be a ring and M a right R-module. Let σ [M] be the full subcategory of Mod-R
subgenerated by M. An M-natural class 𝒦 is a subclass of σ [M] closed under submodules …

The direct sum decomposition of torsion free, ie, nonsingular modules, into direct summands
belonging to saturated classes of modules is developed here for the first time for arbitrary not …

Throughout all rings R are associative wit, h identity, and all modules are unitary right R-
modules. Mod-R will denote the category of unitary right R-modulcs. A classical result in ring …

Throughout, all rings R are associative with identity, and all inodules are unitary right R-
modules. By a class K of modules we inean K is a collection of nlodules such that K is closed …

A pre-natural class of modules over a ring R is one that is closed under isomorphic copies,
submodules, arbitrary direct sums, and certain essential extensions. The set N pr (R) of all …

A right $ R $-module $ M $ is called a generalized qfd module if every M-singular quotient
has finitely generated socle. In this note we give several characterizations to this class of …

An unsaturated class▲ of right R-modules is one that is closed under (a) isomorphic
copies,(b) arbitrary direct sums,(c) essential extensions,(d) essential submodules,(e) and is …

An M-natural class is any subclass of σ [M] which is closed under (1) submodules,(2)
isomorphic copies,(3) direct sums and (4) M-injective envelopes. Let 𝒞 be any set of …