Journal of Commutative Algebra

A universal coefficient theorem for Gauss's lemma

William Messing and Victor Reiner

Full-text: Open access

Article information

Source
J. Commut. Algebra, Volume 5, Number 2 (2013), 299-307.

Dates
First available in Project Euclid: 12 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.jca/1376328034

Digital Object Identifier
doi:10.1216/JCA-2013-5-2-299

Mathematical Reviews number (MathSciNet)
MR3096905

Zentralblatt MATH identifier
1271.13053

Subjects
Primary: 13P05: Polynomials, factorization [See also 12Y05] 14Q20: Effectivity, complexity 12Y05: Computational aspects of field theory and polynomials

Keywords
Gauss lemma constructive

Citation

Messing, William; Reiner, Victor. A universal coefficient theorem for Gauss's lemma. J. Commut. Algebra 5 (2013), no. 2, 299--307. doi:10.1216/JCA-2013-5-2-299. https://projecteuclid.org/euclid.jca/1376328034


Export citation

References

  • B. Banaschewski, The power of the ultrafilter theorem, J. Lond. Math. Soc. 27 (1983), 193-202.
  • T. Coquand, L. Ducos, H. Lombardi and C. Quitté, L'idéal des coefficients du produit de deux polynômes, Rev. Math. Enseign. Sup. 113 (2003), 25-39.
  • J.D. Halpern and A. Levy, The Boolean prime ideal theorem does not imply the axiom of choice, Axiomatic set theory, Proc. Symp. Pure Math. 13, 83-134, American Mathematical Society, 1971.
  • W. Hodges, Six impossible rings, J. Algebra 31 (1974), 218-244.
  • –––, Krull implies Zorn, J. Lond. Math. Soc. 19 (1979), 285-287.
  • H. Lombardi and C. Quitté, Algèbre commutative: Méthodes constructives, Modules projectifs de type fini, Calvage and Mounet, 2011.
  • N.H. McCoy, Remarks on divisors of zero, Amer. Math. Month. 49 (1942), 286-295.
  • M. Nagata, Local rings, Inter. Tracts Pure Appl. Math. 13, Interscience Publishers, a division of John Wiley & Sons, New York, 1962.
  • J.-P. Olivier, Anneaux absolument universel et epimorphismes à but reduit, Exposé VI in Séminaire d`Algèbre Commutative dirigé par Pierre Samuel: 1967/1968. Les épimorphismes d'anneaux, Secr. math., Paris, 1968 (MR # 0245561).
  • N. Popescu and C. Vraciu, Sur la structure des anneaux absoluments plats commutatifs, J. Algebra 40 (1976), 364-383.
  • Y. Rav, Variants of Rado's selection lemma and their applications, Math. Nachr. 79 (1977), 145-165.
  • F. Richman, Nontrivial uses of trivial rings, Proc. Amer. Math. Soc. 103 (1988), 1012-1014.
  • –––, A division algorithm, J. Alg. Appl. 4 (2005), 441-449.
  • D. Scott, Prime ideal theorems for rings, lattices, and Boolean algebras, Bull. Amer. Math. Soc. 60 (1954), 390.
  • M.H. Stone, The theory of representations of Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), 37-111. \noindentstyle