Purely C2 and purely C3 modules and their generalizations, By Najmeh Dehghani

Research

Title	Purely C2 and purely C3 modules and their generalizations
Type	Article
Keywords	Closed submodule; continuous module; direct summand; g.p.continuous module; g.p.quasi-continuous module; pure submodule; p.continuous module; p.quasi-continuous module; quasi-continuous module; von Neumann regular ring
Journal	COMMUNICATIONS IN ALGEBRA
DOI	doi.org/10.1080/00927872.2026.2660856
Researchers	Rasoul Moradi (First researcher) , Najmeh Dehghani (Second researcher) , Yaser Tolooei (Third researcher)

Abstract

The notion of extending modules has been generalized to purely extending, by John Clark. We generalize the notions of C2 and C3, via two ways, by using purity. We say that a module MR has P.C2 (G.P.C2) property if every submodule isomorphic to a pure submodule (direct summand) of MR is a pure submodule. Moreover, we say that a module MR has P.C3 (G.P.C3) property whenever the sum of two independent pure submodules (direct summands) of MR is a pure submodule. We study general properties of these modules and investigate the relations between them.