The category of unital modules over a ring with identity element is characterized as a
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …

We have widely extended the Krull-Remak-Schmidt-Azumaya's theorem in [4],[5],[6],[7],[8]
and [11] and succeeded to prove some of main theorems by virtue of the theory of category …

The notion of Morita-like equivalence has been introduced by Xu, Shum and Turner-Smith in
[13]. Their definition extends the usual Morita equivalence for unital rings to a wider subclass …

Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

Let A, be a ring with identity and AW a cogenerator in the category of unitary, left A-modules,
and denote by B= End (AW) the endomorphism ring of; AW. Then W is regarded as an AB …

The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …

For an arbitrary ring R (always associative with 1) we denote by Mod R th category of all left
R-modules and by mod R the full subcategory of Mod R wi objects the finitely presented …

We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

On splitting of module categories Page 1 Math. Z. t11, 145-150 (1969) On Splitting of Module
Categories HIROYUKI TACHIKAWA Let R be a ring and 9XR the category of all right …