Let R be local Noetherian ring of depth at least two. We prove that there are indecomposable R-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.

Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

The property that an ideal whose annihilator is zero contains a regular element is examined from the point of view of constructive mathematics. It is shown that this property holds for nitely presented algebras over discrete elds, and for coherent, Noetherian, strongly discrete rings that contain an in nite eld. Let R be a commutative ring and M an R-module. For any subset I of R, we write AM(I...

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.

In this paper we make some computations in homological algebra using Gröbner bases for modules over polynomials rings with coefficients in a Noetherian commutative ring. In particular, we show easy procedures for computing the Ext and Tor modules.

We improve Kemper's algorithm for the computation of a Noetherian normalization of the invariant ring of a nite group. The new algorithm, which still works over arbitrary coeecient elds, no longer relies on algorithms for primary decomposition.