Let R be a ring with 1# 0. R-Mod (resp. Mod-R} denotes the category of left (resp. rrght) R-
modules. Throughout the entrre article full subcategories of R-Mod (resp. Mod-R) will be …

Given a ring R, denote by mod-R the category of nitely presented right R-modules, the two
functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of …

An exact sequence 0--f L--+ M-+ N-+ 0 of right A-modules (where A is a ring) is called pure if
its exactness is preserved when tensoring it with any left A-module ([3]; cf. also [ZO] for …

In representation theory as well as in other topics of ring theory it is convenient to consider
for a ring R the categories (mod R, Ab)=: D (R) and ((mod R) OP, Ab)=: L (R) of additive …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

Semiperfect modules were introduced by Mares [15] as a generalization of semiperfect
rings: A projective module P is called semiperfect when every quotient of P has a projective …

Cartan and Eilenberg [1, p. 961 call a functor T of several variables right balanced if T
becomes an exact functor of the remaining variables when any covariant variable is …

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 …

(1) There exists an exact embedding functor R-Mod~ S-Mod.(2) There exists a bimodule
sAR such that AR is faithfully flat.(3) There exists a bimodule sBR with BR a (nontrivial) free …

In various questions in ring theory the followin tegory turns out to be useful (cf.[3-S]). For an
arbitrary ring R let mod R be the category of finitely presented right R-modules (viewed as a …