Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented
module. Considering weak supplements instead of supplements we show that weakly …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

In this paper, we describe $ ss $-supplement submodules in terms of a special class of
endomorphisms. Let $ R $ be a ring with semisimple radical and $ P $ be a projective $ R …

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A module M is called an absolute co-coclosed (absolute co-supplement) module if
whenever M∼= T/X the submodule X of T is a coclosed (supplement) submodule of T. are …

We (re) introduce four ideal-related generalizations of classic module-theoretic notions: the
ideal-superfluity, projective ideal-covers, the ideal-projectivity, and ideal-supplements. For a …

Let R be an associative ring with unity and let I be a two-sided ideal of R contained in the
Jacobson radical J (R) of R. For a right module M over the ring R we call the right module …

Title: Compact objects in categories of modules Author: Peter Kálnai Department:
Department of Algebra Supervisor: Mgr. Jan Žemlička, Ph. D., Department of Algebra …

Let R be a ring with Jacobson radical J (R). Given a left R-module M, a supplement
submodule of M is a submodule K≤ M for which there exists K≤ M such M= K+ K and K is …