6 citations · 8 across the 6 of their papers we have counts for
5 papers · 1 filter
Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts
Geoffrey D. Dietz, Rebecca R. G
Let be a commutative, local, Noetherian ring. In a past article, the first author developed a theory of -algebras, termed seeds, that can be mapped to balanced big Cohen-Mac…
Axiomatic Closure Operations, Phantom Extensions, and Solidity
Geoffrey D. Dietz
In this article, we generalize a previously defined set of axioms for a closure operation that induces balanced big Cohen-Macaulay modules. While the original axioms were only defi…
A Characterization of Closure Operations That Induce Big Cohen-Macaulay Modules
Geoffrey D. Dietz
The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module B over a complete local domain R…
Big Cohen-Macaulay Algebras and Seeds
Geoffrey D. Dietz
We delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive…
Tight Closure of Finite Length Modules in Graded Rings
Geoffrey D. Dietz
We look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogene…