Introduction. This paper contains the foundations of a general theory of separable algebras over arbitrary commutative rings. Of the various equivalent conditions for separability in the classicalâ€¦ (More)

The main aim of this paper is to relate almost split sequences to singularity theory by showing that the McKay quiver built from the finite-dimensional representations of a finite subgroup G of GL(2,â€¦ (More)

0â€”>Xnâ€”Â» . . . ~->Xoâ€”Â» Aâ€”>0 where the left /1-modules Xo, . . . , Xn are projective. If no such sequence exists for any n, then 1. dimÎ› A = oo. The left global dimension of A is 1. g\. dim A sup 1.â€¦ (More)

The aim of these notes is to report some new developments on the problem of describing all possible shapes of the connected components of the Auslander-Reiten quiver Î“A of an artin algebra A. Theâ€¦ (More)

Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyxâ€¦ (More)

Let R be a complete local two-dimensional integrally closed noetherian nonregular Gorenstein domain with maximal ideal m over an algebraically closed field k, such that R/m = k. Then the category ofâ€¦ (More)

Let Ã„ be a commutative noetherian ring and i: R â€”Â» A an Ralgebra such that A is a finitely generated /Â¿-module. Then the annihilator of A in R is nilpotent if and only if the cokernel of the inducedâ€¦ (More)