A module is defined to be an automorphism-invariant module if it is invariant under
automorphisms of its injective hull. Quasi-injective modules and, more generally, pseudo …

Let R be an associative ring with unity. A unital left R-module M is said to be distributive if for
every submodules S, T and U of M, the equality S∩(T+ U)= S∩ T+ S∩ U holds true. In this …

We establish equivalent conditions under which every object in an Abelian category has a
monic X-cover and an epic X-envelope respectively, when X is a class of objects closed …

In this paper, the concept of iso-DICC modules is introduced and extensively investigated.
These modules are the generalization of DICC, iso-Noetherian and iso-Artinian modules …

Torsion theories are a pinnacle in the theory of abelian categories. They are a
generalization of torsion abelian groups and in this generalization one of the most studied is …

In this article, we introduce the concept of parallel Krull dimension of a module (briefly, p.
Krull dimension), which is Krull-like dimension extension of the concept of DCC on poset of …

Let $ R $ be a ring and $ M $ be an $ R $-module. Two modules $ A $ and $ B $ are called
orthogonal, written $ A\perp B $, if they do not have non-zero isomorphic submodules. We …

‌In this paper we continue our study of perpendicular graph of modules‌, ‌that was introduced
in\cite {Hokkaido} ‌. ‌Let $ R $ be a ring and $ M $ be an $ R $-module‌. ‌Two modules $ A …

In this work, we consider the existence and construction of pseudocomplements in some
lattices of module classes. The classes of modules belonging to these lattices are defined …

Some properties of and relations between several (big) lattices of module classes are used
in this paper to obtain information about the ring over which modules are taken. The authors …