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• W2921761187 abstract "The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a constructive meaning to ideal objects is a problem which dates back to Hilbert's program, and today is still a central theme in the area of dynamical algebra, which focuses on the elimination of ideal objects via syntactic methods. In this paper, we take an alternative approach based on Kreisel's no counterexample interpretation and sequential algorithms. We first give a computational interpretation to an abstract maximality principle in the countable setting via an intuitive, state based algorithm. We then carry out a concrete case study, in which we give an algorithmic account of the result that in any commutative ring, the intersection of all prime ideals is contained in its nilradical." @default.
• W2921761187 created "2019-03-22" @default.
• W2921761187 creator A5035502484 @default.
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• W2921761187 creator A5072068171 @default.
• W2921761187 date "2019-03-07" @default.
• W2921761187 modified "2023-10-01" @default.
• W2921761187 title "An algorithmic approach to the existence of ideal objects in commutative algebra" @default.
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• W2921761187 hasPublicationYear "2019" @default.
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