B. Olberding

activity

20122017

most citedDe-noetherizing Cohen-Macaulay rings

1 citations · 1 across the 3 of their papers we have counts for

collaborators

7 papers

math.AC2017★ 1 cited

De-noetherizing Cohen-Macaulay rings

Laszlo Fuchs, Bruce Olberding

We introduce a new class of commutative {non-noetherian} rings, called $n$ -subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. F…

math.AC2017

On the topology of valuation-theoretic representations of integrally closed domains

Bruce Olberding

Let $F$ be a field. For each nonempty subset $X$ of the Zariski-Riemann space of valuation rings of $F$ , let $A (X) = ⋂_{V \in X} V$ and ${J}(X) = \bigcap_{V \in X}{\mathfrak…

math.AC2017

Noetherian intersections of regular local rings of dimension two

William Heinzer, Bruce Olberding

Let $D$ be a 2-dimensional regular local ring and let $Q (D)$ denote the quadratic tree of 2-dimensional regular local overrings of $D$ . We examine the Noetherian rings that are int…

math.AC2017

A principal ideal theorem for compact sets of rank one valuation rings

Bruce Olberding

Let $F$ be a field, and let Zar $(F)$ be the space of valuation rings of $F$ with respect to the Zariski topology. We prove that if $X$ is a quasicompact set of rank one valuation r…

math.AC2017

Directed unions of local quadratic transforms of regular local rings and pullbacks

Lorenzo Guerrieri, William Heinzer, Bruce Olberding +1

Let ${R_{n}, m_{n}}_{n \geq 0}$ be an infinite sequence of regular local rings with $R_{n + 1}$ birationally dominating $R_{n}$ and $m_{n} R_{n + 1}$ a principal idea…

math.AC2016

One-dimensional stable rings

Bruce Olberding

A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. The class of stable rings include…