Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

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 …

The development of a general theory of rings of quotients may be said to have started with
the construction by Johnson [1] of the maximal ring of quotients Q max of a non-singular ring …

The purpose of this paper is to study further the ideal and module structure of a commutative
ring with identity, in which every principal ideal is projective. Results concerning particular …

THEOREM L (a) A right R-module A is finitely generated if and only if for any collection {Ca}
of left R-modules, the natural map A (x) ΠCa-+ Π (A® Ca) is surjective.(b) A right R-module A …

Let K be a convex set in a lcs and A a convex subset in the closure of K. It is shown in § 1
that, in certain cases, the exposed points of A belong to the sequential closure of K …

Our main aim in this article is to settle this question by showing that the above ring is never a
self-injective ring. Using a result of Osofsky [ll] and a result in [12] we immediately observe …

INTRODUCTION Let R be a ring and R-Mod the category of left R-modules. If F is a left
Gabriel topology on R, then there is an associated quotient category (R, F)-~ od which is the …

Let Rbe a ring with identity. Chase [5] has characterized the right coherent rings; he has
shown that arbitrary products of RR are flat if and only if finitely generated submodules of …

T (M)=(x= M| Hom,(Ra, I (R))= 0) where I (R) is the injective hull of R as a left R-module. A left
R-module M is said to be torsion free if T (M)= 0. For the properties of torsion free modules …