Gorenstein derived functors

Derived Functors

Derived equivalences and Gorenstein algebras

In this note, we introduce the notion of Gorenstein algebras. Let R be a commutative Gorenstein ring and A a noetherian R-algebra. We call A a Gorenstein R-algebra if A has Gorenstein dimension zero as an R-module (see [2]), add(D(AA)) = PA, where D = HomR(−, R), and Ap is projective as an Rpmodule for all p ∈ Spec R with dim Rp < dim R. Note that if dim R = ∞ then a Gorenstein R-algebra A is p...

Composite Cotriples and Derived Functors

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the structure of a DG-algebra and resolved by the ...

Non-additive Functors, Their Derived Functors, and the Suspension Homomorphism.

3E. L. Post, J. Symb. Logic, 12, 1-11, 1947. 4In the sense of Post, the word problem for Z is reducible to that for sp (2:). 5 W. Magnus, Math. Annalen, 106, 295-307, 1932. 6 DanaScott, abstract, J. Symb. Logic, 21, 111-112, 1956. 7Marshall Hall, J. Symb. Logic, 14, 115-118, 1949. 8 G. Higman, B. H. Neumann, and H. Neumann, J. London Math. Soc., 24, 247-254, 1949. 9 As defined, UG, Part I, p. 2...

Gorenstein Model Structures and Generalized Derived Categories

In [Hov02], the second author introduced the Gorenstein projective and Gorenstein injective model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring. These two model structures are Quillen equivalent and in fact there is a third equivalent structure we introduce; the Gorenstein flat model structure. The homotopy category with respect to each of these is called the st...