AX we denote by pdA X (resp. idA X) the projective (resp. injective) dimension of X. With D=
Homk (−, k) we denote the standard duality with respect to the ground field. Then AD (AA) is …

Let A be a finite-dimensional¿-algebra over an algebraically closed field k. We denote by
mod A the category of finitely generated left^ 4-modules. For an^-module AX we denote by …

In this sketch, I will try to indicate how cardinality questions and manipulations became
intimately connected with homological algebra. The modern form of this subject stems from …

Let A be a finite-dimensional k-algebra (associative, with unit) over some fixed algebraically
closed field k. Let mod A be the category of finitely generated left A-modules. With D= Hom k …

1.1. Let k be a ring and let C (k) be the category of (unbounded) complexes of k-modules. As
we know from Spaltenstein [Sp](see also [AFH] and [BL]) one can do a homological algebra …

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 …

Let R be a ring with identity, and let C be a small, nonempty category. We denote the
category of right R-modules by AbR and the category of contravariant functors C→ AbR by …

Although it is not. true that the section functor r'a with support in the variety of the ideal a
takes a bounded complex of flat modules into a bounded complex of flat modules, a …

The study of the stable derived category of a finite-dimensional self-injec-tive algebra A over
a field k was begun in [7, 8]. As the name suggests, this category can be regarded as a sort …

The Yoneda definition of Ext”(A, C) in terms of exact sequences of length n from C to A
[Z4],[Z5], enables one to define the homological dimension of a nonzero object A (hd A) in …