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

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 …

ON RINGS WHOSE LEFT MODULES ARE MODULES Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 54, January 1976 ON RINGS WHOSE LEFT …

It is shown that the rings $ R $ all of whose left modules are direct sums of finitely generated
modules satisfy the following finiteness condition: For each positive integer $ n $ there are …

The idea of purity pervades human culture, from religion through sexual and moral codes,
cleansing rituals and dietary rules, to stratifications of societies into castes. It does so to an …

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a
direct sum of modules with local endomorphism rings if and only if every direct sum of copies …

Let R be a left pure-semisimple ring. It is proved that if R has self-duality or if R is a
polynomial identity ring, then R is of finite representation type. If there exists an example of a …

We investigate the rings over which every countably generated module is pure-projective
and generalize the theory of rings of pure global dimension zero. This class of rings is …

Ž. We recall that a ring R with identity is said to be of finite representation type if it is right
artinian and has only finitely many isomorphism Ž. Ž classes of finitely generated …

In this paper, by using functor rings and functor categories, we study finiteness and purity of
subcategories of the module categories. We give a characterisation of contravariantly finite …