We study almost Dedekind domains with respect to the failure of ideals to have radical
factorization, that is, we study how to measure how far an almost Dedekind domain is from …

We generalize the concept of localization of a star operation to flat overrings; subsequently,
we investigate the possibility of representing the set Star(R) of star operations on R as the …

Let F be a field, and let Zar (F) be the space of valuation rings of F with respect to the Zariski
topology. We prove that if X is a quasicompact set of rank one valuation rings in Zar (F) …

We prove a necessary and sufficient criterion for the ring of integer‐valued polynomials to
behave well under localization. Then, we study how the Picard group of Int (D) and the …

This paper contributes to the study of the core of an ideal in integral domains. Our aim is to
develop explicit formulas for the core in various classes of Prüfer domains. We pay particular …

We introduce the concept of pre-Jaffard family, a generalization of Jaffard families obtained
by substituting the locally finite hypothesis with a much weaker compactness hypothesis …

Motivated by recent work on the use of topological methods to study collections of rings
between an integral domain and its quotient field, we examine spaces of subrings of a …

Let $ D $ be a Dedekind domain with finite residue fields. We provide topological insights
into certain classes of ideals of $ Int (D) $ lying over a given maximal ideal $\mathfrak m $ of …

Given an integral domain D and a D-algebra R, we introduce the local Picard group LPic (R,
D) as the quotient between the Picard group Pic (R) and the canonical image of Pic (D) in …

We study the set of localizations of an integral domain from a topological point of view,
showing that it is always a spectral space and characterizing when it is a proconstructible …