The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the
construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really …

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 recent paper by Goro Azumaya on M-projective and M-injective modules [1] suggests a
generalization of the concept of hereditary rings to modules which is also capable of …

This is the first book on the subject of FPF rings and the systematic use of the notion of the
generator of the category mod-R of all right R-modules and its relationship to faithful …

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 …

Let R be an associative ring with identity, and let denote the category of unital left R-
modules. It is known that if R is a commutative, Noetherian ring, then the maximal torsion …

Given any injective module IR, its bicommutator S contains as a subring the ring Q of
quotients of R relative to the largest torsion theory for which IR is torsionfree. Q is even a …

Any injective module F'E R-Mod defines a torsion radical (torsion theory) and an associated
quotient category R-Mod/V, which is a hli reflective Grothendieck subcategory of R-Mod with …

We consider the module, injective with respect to the pair, where, and form the ring by
constructing rings of quotients with respect to torsion. We find necessary and sufficient …

The survey is chiefly devoted to the materials in articles reviewed in Referativnyi Zhurnal"
Matematika" during 1969-1972 and closely abuts the surveys [28, 29, 15] which have …