Abstract
We define a universal star operation to be an assignment *: A ↦ * A of a star operation * A on A to every integral domain A. Prime examples of universal star operations include the divisorial closure star operation v, the t-closure star operation t, and the star operation w = F ∞ of Hedstrom and Houston. For any universal star operation *, we say that an extension B ⊃ A of integral domains is *-ideal class linked if there is a group homomorphism Cl* A (A) → Cl* B (B) of star class groups induced by the map I ↦ (IB)* B on the set of * A -ideals I of A. We study several natural subclasses of the class of *-ideal class linked extensions.
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