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

A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

We introduce the notions of Baer and quasi-Baer properties in a general module theoretic
setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) left ideal of …

A module M is called extending if every submodule of M is essential in a direct summand.
We call a module FI-extending if every fully invariant submodule is essential in a direct …

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …

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 …

It is proved, among other results, that a prime right nonsingular ring (in particular, a simple
ring) R is right self-injective if RR is invariant under automorphisms of its injective hull. This …

This book is an introduction to the theory of rings and modules that goes beyond what one
normally obtains in a graduate course in abstract algebra. The theme of the text is the …

A module is extending (or CS, C1) if every complement submodule is a direct summand or,
equivalently, every submodule is essential in a direct summand. The terms extending and …