Motivated by their impact on homological algebra, the change of rings results have been the subject of several interesting works in Gorenstein homological algebra over Noetherian rings. In this paper, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, sec...

A number of examples and constructions of local Noetherian domains without finite normalization have been exhibited over the last seventy-five years. We discuss some of these examples, as well as the theory behind them.

A number of results are proved concerning the Quillen ^-theory K+(S*G) of the skew group ring S*G, where S is a Noetherian ring and G is a finite group of automorphisms of 5. Applications are given to the computation of AT-groups of group algebras and of equivariant /^-theory for affine varieties.

We survey and extend recent work on integrally closed overrings of two-dimensional Noetherian domains, where such overrings are viewed as intersections of valuation overrings. Of particular interest are the cases where the domain can be represented uniquely by an irredundant intersection of valuation rings, and when the valuation rings can be chosen from a Noetherian subspace of the Zariski-Rie...

In this note we improve and extend duality theorems for crossed products obtained by M. Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case of an arbitrary Noetherian commutative ground rings under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary Noetherian ground rings.

Abstract We uncover a connection between the model-theoretic notion of superstability and that noetherian rings pure-semisimple rings. characterize via class left modules with embeddings. Theorem 0.1 For ring R following are equivalent. (1) is noetherian. (2) The R-modules embeddings superstable. (3) every ? ? | + ? 0 , there ? such has uniqueness limit models cardinality ?. (4) Every model in ...