On algebraic models for homotopy 3-types.
On Arens-Michael algebras which do not have non-zero injective ⨶-modules
A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in , algebras of smooth functions on domains in , algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.
On Auslander–Reiten components for quasitilted algebras
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander-Reiten quiver of a quasitilted algebra A.
On Auslander-Reiten translates in functorially finite subcategories and applications
We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when this category...
On categorical crossed modules.
On Central Group Extensions and Homology
On Cohen-Macaulay rings
In this paper, we use a characterization of -modules such that to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting to be the local cohomology functor of with respect to the maximal ideal where is the Krull dimension of .
On Cohomological Equivalence.
On cohomological periodicity for infinite groups.
On cohomology of graded group categories
On Convergence of Spectral Sequences.
On derived categories and derived functors.
On distributive homological algebra, I. RE-categories
On distributive homological algebra, II. Theories and models
On distributive homological algebra. III. Homological theories
On exactness of long sequences of homology semimodules.
On Filtered Modules and their Associated Graded Modules.
On flat covers in varieties
Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers.
On -disconnected injective models
Let be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the -connected case is incorrect because of an error concerning algebraic properties. In the -disconnected case the orbit category was originally replaced by the category with one object for each component of each fixed point simplicial subsets of a -simplicial set , for all subgroups . We redefine the equivariant minimality and redevelop some results on the rational homotopy...
On Galois descent for Hochschild and cyclic homology.