An important part of homological algebra deals with modules possessing projective
resolutions of finite length. This goes back to Hilbert's famous theorem on syzygies through …

In this book, the authors present both traditional and modern discoveries in the subject area,
concentrating on advanced aspects of the topic. Existing material is studied in detail …

A number of sophisticated people tend to disparage category theory as consistently as
others disparage certain kinds of classical music. When obliged to speak of a category they …

Mod ª Ex C, Ab, M¬ Hom y, M my Ž. Ž. Ž. is an equivalence. Thus we can replace a-module
by an exact functor Ž. op C ª Ab. Of course, since the work of Auslander, it has been common …

We study the homotopy category of unbounded complexes with bounded homologies and
its quotient category by the homotopy category of bounded complexes. In the case of the …

Injective covers of modules were introduced by Enochs [5] as a categorical dual of an
injective envelope and they have been investigated by many authors. The T-torsionfree …

Elementary duality between left and right modules over a ring, especially its interpretation in
terms of the relevant functor categories, is discussed, as is the relationship between these …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

The main results of this paper concern decompositions of an injective module, either as a
direct sum of submodules or as the injective envelope of a direct sum of injective …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …