Some remarks on star operations and the class group
This paper gives a result concerning when for a fixed star operation * on a commutative ring R, ACC holds for integral *-ideals. - A second theorem shows that two *-ideals are equal if they are equal at certain localizations. That theorem is then used to show that in the domain D, if S is a multiplicatively closed subset generated by principal primes, then \(Pic(D)\to Pic(D_ S)\) and \(Cl_ t(D)\to Cl_ t(D_ S)\) are both injective. (Here, \(Cl_ t(D)=T(D)/\Pr in(D)\), and T(D) is the group of t-invertible t-ideals, the t-operation being a well known star- operation.)
scientific article; zbMATH DE number 4063228
scientific article