A duality between two categories C and 3) is an equivalence of categories between the dual
category Cop of C and 3). The idea of studying dualities between full subcategories of …

In his paper [191 Morita introduced the concept of functorial dualities between two full
subcategories A& and.+? of the categories of right R-modules and left S-modules containing …

S Q-reflexive modules of R-Mod and Mod-S. In that work the authors give necessary and
sufficient conditions on Q for S being right semihereditary or coherent. Nevertheless the …

Let R and S be rings and let RW s be a bimodule. We shall denote both the functors HomÄ
(_, W): i?-Mod-> Mod-S and Homs (_, W): Mod-S->/?-Mod by Aw and the composition of the …

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 …

The study of dualities between categories of modules generalizing Morita duality cannot
dispense with the use of topologies (see [1, 2, 3, 7, 8]). In this paper we try to give a new …

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 …

Given a ring (associative with identity) we denote by Mod () the category of (right)-modules
and by mod () the full subcategory of all nitely presented-modules. Our aim in this note is to …

At the spring meeting of the Mathematical Society of Japan, in 1968, professors K. Morita
and H. Tachikawa gave a lecture entitled “On semiprimary QF-3 rings,” in which they have …

It is known that if R is a ring with identity, and S and A op are the functor rings associated to
the categories Mod (R) and Mod (R op), respectively, then there is a duality between the …