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21 papers
The Golomb topology of polynomial rings, II
Dario Spirito
We study the interplay of the Golomb topology and the algebraic structure in polynomial rings over a field . In particular, we focus on infinite fields of positive ch…
Localizations of integer-valued polynomials and of their Picard group
Dario Spirito
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 …
The derived sequence of a pre-Jaffard family
Dario Spirito
We introduce the concept of \emph{pre-Jaffard family}, a generalization of Jaffard families obtained by substituting the locally finite hypothesis with a much weaker compactness hy…
Asymptotic for the number of star operations on one-dimensional Noetherian domains
Dario Spirito
We study the set of star operations on local Noetherian domains of dimension such that the conductor (where is the integral closure of ) is equal to the maxi…
The Golomb topology of polynomial rings
Dario Spirito
We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show t…
Multiplicative closure operations on ring extensions
Dario Spirito
Let be a ring extension and be a set of -submodules of . We introduce a class of closure operations on (which we call \emph{multipl…