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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References
Buchsbaum D.A., Eisenbud D.: What makes a complex exact. J. Algebra 25, 259–268 (1973)
Buchsbaum D.A., Eisenbud D.: Some structure theorems for finite free resolution. Adv. Math. 12, 84–139 (1974)
Cayley A.: On the theory of elimination. Camb. Dublin Math. J. 3, 116–120 (1848)
Coquand Th., Lombardi H.: A logical approach to abstract algebra. Math. Str. Comput. Sci. 16, 885–900 (2006)
Eagon J.A., Northcott D.G.: On the Buchsbaum-Eisenbud theory of finite free resolution. J. Reine Angew. Math. 262/263, 205–219 (1973)
Mines R., Richman F., Ruitenburg W.: A Course in Constructive Algebra. Univeristext. Springer, Berlin (1988)
Northcott D.G.: Finite Free Resolutions. Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (1976)
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Coquand, T., Quitté, C. Constructive finite free resolutions. manuscripta math. 137, 331–345 (2012). https://doi.org/10.1007/s00229-011-0466-5
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DOI: https://doi.org/10.1007/s00229-011-0466-5