Journal Article10.1007/S00229-011-0466-5
Constructive Finite Free Resolutions
Thierry Coquand,Claude Quitté +1 more
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TL;DR: In this paper, the authors simplify the proofs of these results, which become now elementary in a logical sense (no use of prime ideals, or minimal prime ideals) and, we hope, more perspicuous.
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Abstract: Northcott’s book Finite Free Resolutions (1976), as well as the paper (J. Reine Angew. Math. 262/263:205–219, 1973), present some key results of Buchsbaum and Eisenbud (J. Algebra 25:259–268, 1973; Adv. Math. 12: 84–139, 1974) both in a simplified way and without Noetherian hypotheses, using the notion of latent nonzero divisor introduced by Hochster. The goal of this paper is to simplify further the proofs of these results, which become now elementary in a logical sense (no use of prime ideals, or minimal prime ideals) and, we hope, more perspicuous. Some formulations are new and more general than in the references (J. Algebra 25:259–268, 1973; Adv. Math. 12: 84–139, 1974; Finite Free Resolutions 1976) (Theorem 7.2, Lemma 8.2 and Corollary 8.5).
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Citations
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References
A logical approach to abstract algebra
Thierry Coquand,Henri Lombardi +1 more
TL;DR: This work uses a general method to transform some logically complex first-order formulae into a geometrical form and presents an example where the simplification was significant enough to suggest an improved version of a classical theorem.
A logical approach to abstract algebra
Thierry Coquand
- 08 Jun 2005
TL;DR: This work uses a general method to transform some logically complex first-order formulae in a geometrical form which may be interesting in itself and presents an example where the simplification was significant enough to suggest an improved version of a classical theorem.
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