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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…
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…