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 product of Star(T), as T ranges over a family of overrings of R with special properties. We then apply this method to study the set of star operations on a Priffer domain R, in particular the set of stable star operations and the star-class groups of R.
Jaffard families and localizations of star operations
Spirito, D
2019
Abstract
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 product of Star(T), as T ranges over a family of overrings of R with special properties. We then apply this method to study the set of star operations on a Priffer domain R, in particular the set of stable star operations and the star-class groups of R.
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