This monograph first published in 1986 is a reasonably self-contained account of a large
part of the theory of non-commutative Noetherian rings. The author focuses on two important …

This paper is expository in nature, although several results (including 1.5, 1.6 (2), 2.7 and
3.1) appear to be new, and continues the account of localization for noncommutative rings …

A module wilpl be called finitely annihilated if its annihilator is the annihilator of a finite
subset. A ring is Artinian if and only if every module over it is finitely annihilated. This …

The general theory of localization, developped by Rattray and the author [19] from a method
of Fakir [7], yields not only the localization of Bourbaki-Gabriel [2]? but also the Iocalization …

Lambek and Michler [7] and Jategaonkar 14, 5] have studied a notion of localization at a
semiprime ideal I of a left Noetherian ring R. The purpose of this paper is to extend certain of …

Let R be an associative ring with identity, and let denote the category of unital left R-
modules. The Walkers [6] raised the question of characterizing the maximal torsion radicals …

A survey is given of results on modules over rings, covering 1976–1980 and continuing the
series of surveys “Modules” in Itogi Nauki.

The concept of reduced rank has been a useful tool in studying Noetherian rings, orders in
Artinian rings, and rings with Krull dimension. These classes of rings have been …

I f A has some additional properties, then L (J) and sL (5) are reflective subcategories and
the reflector R into L (J) preserve, s regular monomorphisms. R considered as an …

A definition of torsion theory T on the category R-mod of left R-modules is given, using an
equivalence relation on the class of all injective left R-modules. For a torsion theory T, the …