2 citations · 3 across the 25 of their papers we have counts for
30 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…
A connectedness theorem for spaces of valuation rings
William Heinzer, K. Alan Loper, Bruce Olberding +1
Let be a field, let be a local subring of , and let Val be the space of valuation rings of that dominate . We lift Zariski's connectedness theorem for fibe…
The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two
Bruce Olberding, William Heinzer
Let be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate . We restrict to the…
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…
Noetherian intersections of regular local rings of dimension two
William Heinzer, Bruce Olberding
Let be a 2-dimensional regular local ring and let denote the quadratic tree of 2-dimensional regular local overrings of . We examine the Noetherian rings that are int…