3 citations · 5 across the 8 of their papers we have counts for
8 papers
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…
Non-integrally closed Kronecker function rings and integral domains with a unique minimal overring
Lorenzo Guerrieri, K. Alan Loper
It is well-known that an integrally closed domain can be express as the intersection of its valuation overrings but, if is not a Prüfer domain, the most of valuation overri…
On the integral domains characterized by a Bezout Property on intersections of principal ideals
Lorenzo Guerrieri, K. Alan Loper
In this article we study two classes of integral domains. The first is characterized by having a finite intersection of principal ideals being finitely generated only when it is pr…
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…
Ultrafilter and Constructible topologies on spaces of valuation domains
Carmelo A. Finocchiaro, Marco Fontana, K. Alan Loper
Let be a field and let be a subring of . We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space…
Cancellation properties in ideal systems: an not star operation
Marco Fontana, K. Alan Loper, Ryûki Matsuda
We show that Krull's \texttt{a.b.} cancellation condition is a properly stronger condition than Gilmer's \texttt{e.a.b.} cancellation condition for star operations.