We generalize the concept of localization of a star operation to flat overrings; subsequently, we investigate the possibility of representing the set $insstar(R)$ of star operations on $R$ as the product of $insstar(T)$, as $T$ ranges in a family of overrings of $R$ with special properties. We then apply this method to study the set of star operations on a Pr"ufer domain $R$, in particular the set of stable star operations and the star-class groups of $R$.
Spirito, D. (2019). Jaffard families and localizations of star operations. JOURNAL OF COMMUTATIVE ALGEBRA, 11(2), 265-300 [10.1216/JCA-2019-11-2-265].
Jaffard families and localizations of star operations
Dario Spirito
2019-01-01
Abstract
We generalize the concept of localization of a star operation to flat overrings; subsequently, we investigate the possibility of representing the set $insstar(R)$ of star operations on $R$ as the product of $insstar(T)$, as $T$ ranges in a family of overrings of $R$ with special properties. We then apply this method to study the set of star operations on a Pr"ufer domain $R$, in particular the set of stable star operations and the star-class groups of $R$.File in questo prodotto:
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