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 …

By using the correspondence between locally finitely presented additive categories and
rings with enough idempotents, we study several properties of such rings in terms of the …

Let C be a subcategory of the category of finitely generated R-modules over a commutative
noetheian ring R. We prove that, if C is closed under images and extensions (which we call …

Equivalence and Duality of Quotient Categories (4 C21). Page 1 JOURNAL OF ALGEBRA 143,
144-155 (1991) Equivalence and Duality of Quotient Categories ZHOU ZHENGPING …

Let R-Mod be the category of unital left modules over a ring R. It is shown that a finitely
closed subcategory K of R-Mod is an AB5∗ category if and only if K is dual to some finitely …

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 …

In this paper, we prove a version of Freyd's generating hypothesis for triangulated
categories: if D is a cocomplete triangulated category and S∈ D is an object whose …

A ringoid is a small (pre) additive category. A ring can be viewed as a ringoid with only one
object. Many facts about rings generalize to yield facts about ringoids. The advantage of …

Over any left and right self-injective ring R the R-dual functors ()* between R-Mod and Mod-
R are exact, and hence so are the double R-dual functors ()** on each of these categories. In …

A contra variant category-equivalence between categories of right R-modules and left S-
modules (all rings have units, all modules are unitary) that contain RR, SS and are closed …