A universal algorithm for Krull's theorem

Powell, Thomas; Schuster, Peter und Wiesnet, Franziskus (2022): A universal algorithm for Krull's theorem. In: Information and Computation, Bd. 287, 104761

Abstract

We give a computational interpretation to an abstract formulation of Krull's theorem, by analysing its classical proof based on Zorn's lemma. Our approach is inspired by proof theory, and uses a form of update recursion to replace the existence of maximal ideals. Our main result allows us to derive, in a uniform way, algorithms which compute witnesses for existential theorems in countable abstract algebra. We give a number of concrete examples of this phenomenon, including the prime ideal theorem and Krull's theorem on valuation rings. (C) 2021 Elsevier Inc. All rights reserved.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0890-5401
• Sprache: Englisch