2 citations · 3 across the 5 of their papers we have counts for
5 papers
Interval Rings
William Heinzer, K. Alan Loper, Bruce Olberding +1
Interval rings comprise a class of one-dimensional integrally closed local integral domains which are overrings of a two-dimensional regular local ring. We construct them by inters…
Connectedness and integrally closed local overrings of two-dimensional regular local rings
William Heinzer, K. Alan Loper, Bruce Olberding +1
Let be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of that dominat…
The tree of quadratic transforms of a regular local ring of dimension two
William Heinzer, K. Alan Loper, Bruce Olberding
Let be a 2-dimensional regular local ring and let denote the quadratic tree of 2-dimensional regular local overrings of . We explore the topology of the tree a…
An infinite cardinal-valued Krull dimension for rings
K. Alan Loper, Zachary Mesyan, Greg Oman
We define and study two generalizations of the Krull dimension for rings, which can assume cardinal number values of arbitrary size. The first, which we call the "cardinal Krull di…
Ideal theory of infinite directed unions of local quadratic transforms
W. Heinzer, K. A. Loper, B. Olberding +2
Let be a regular local ring of dimension at least 2. Associated to each valuation domain birationally dominating , there exists a unique sequence of local quadrati…