The term The Theory of Rings seems first used as title of a book by Jacobson [43], and in his
preface Jacobson asserts that the theory that forms the subject of the book had its beginning …

A left module M over a ring R is cofaithful in case there is an embedding of R into a finite
product of copies of M. Our main result states that a semiprime ring R is left Goldie, that is …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

In a category of modules the notions of ρ-injectivity (with respect to a torsion radical ρ) and
quasi-injectivity can be generalized to a notion of injectivity with respect to two preradicals …

We define below a notion for modules which is dual to that of faithful, and a notion of “fully
divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful …

For an arbitrary R-module M we consider the radical (in the sense of Maranda) GM, namely,
the largest radical among all radicals G, such that G (M). We determine necessary and …

WE SHALL assume that all rings under consideration are associative rings with identity, and
that all modules are unital. We show that a ring R is a prime ring if and only if every nonzero …

Первичные градуированные модули∗ Page 1 Первичные градуированные модули∗ ИНБАЛАБА
Тульский государственный педагогический университет им. ЛНТолстого e-mail: ibalaba@tula.net …

Generalized monoform and quasi injective modules Page 1 Pacific Journal of Mathematics
GENERALIZED MONOFORM AND QUASI INJECTIVE MODULES JOHN DAUNS Vol. 66, No …

In [11] we havestudied those rings with trivial preradical ideals. Dually in this paper, we shall
investigate rings for which every nonzero (idempotent, left exact or cohereditary, etc.) …