Functorial Properties of Star Operations |
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Authors: | Jesse Elliott |
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Institution: | 1. California State University, Channel Islands , Camarillo, California, USA jesse.elliott@csuci.edu |
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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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Keywords: | Class group Domain extension Star operation t-linked extension |
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