MMN-5059
Semisimple-continuous modules
Soumitra Das; Yeliz Kara; Özgür Taşdemi̇r;Abstract
An R-module M is said to be a semisimple-continuous module if it is weak CS and
semisimple-direct injective. It is proved that any semisimple-continuous module is decomposed
as a direct sum of a semisimple module and a module with square-free socle. We investigate
when the finite exchange property implies full exchange property for the former class of modules. Moreover, we explore the notion of the semisimple-continuity for Abelian groups. We
also characterize right Noetherian right V-rings in terms of semisimple-continuous modules. Examples are delimit our results.
Vol. 27 (2026), No. 1, pp. 149-165