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 …

Full article: Pure-direct-objects in categories: transfer via functors Skip to Main Content Taylor and
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Full article: Σ-Extending Modules, Σ-Lifting Modules, and Proper Classes Skip to Main
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Let R be a cumulative ring with identity and let M be a unital left R-module. Harada and
Muller introduce the following concept an R-module M is called extending module if every …

In this paper,(dual) purely Rickart objects are introduced as generalizations of (dual) Rickart
objects in Grothendieck categories. Examples showing the relations between (dual) relative …

In this note we consider a generalization of the notion of a purely extending modules,
defined using y–closed submodules. We show that a ring R is purely y–extending if and only …

In this thesis we investigate proper classes of short exact sequences, especially those
proper classes induced by supplement-like and complement-like submodules in the …

We introduce the notions of purely Baer and purely Rickart modules. We provide several
characterizations and investigate properties of each of these concepts. We provide new …

In this paper we study generalizations of the concept of pure-direct-injectivity from module
categories to Grothendieck categories. We examine for which categories or under what …

A purely extending module is a generalization of an extending module. In this paper, we
study several properties of purely extending modules and introduce the notion of purely …