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11 papers · 1 filter
The reciprocal complement of a polynomial ring in several variables over a field
Neil Epstein, Lorenzo Guerrieri, K. Alan Loper
The *reciprocal complement* of an integral domain is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of ar…
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…
Integral closure of rings of integer-valued polynomials on algebras
Giulio Peruginelli, Nicholas J. Werner
Let be an integrally closed domain with quotient field . Let be a torsion-free -algebra that is finitely generated as a -module. For every in we consider i…
Some closure operations in Zariski-Riemann spaces of valuation domains: a survey
Carmelo A. Finocchiaro, Marco Fontana, K. Alan Loper
In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains.
The constructible topology on spaces of valuation domains
Carmelo Finocchiaro, Marco Fontana, K. Alan Loper
We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on an {\sl arbitrary spectral space} and we observe that this top…