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 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 …

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 …

We introduce and study the set of radical semistar operations of an integral domain D. We
show that their set is a complete lattice that is the join-completion of the set of spectral …

The first part of this paper is mostly devoted to survey results by Northcott-Reufel on length
functions over commutative domains, specifically over valuation domains and 1-dimensional …

Let λ be a general length function for modules over a Noetherian ring R. We use λ to
introduce Hilbert series and polynomials for R [X]-modules, measuring the growth rate of λ …