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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On resultants


Author: Gerald Myerson
Journal: Proc. Amer. Math. Soc. 89 (1983), 419-420
MSC: Primary 13B25; Secondary 10M05
DOI: https://doi.org/10.1090/S0002-9939-1983-0715856-2
MathSciNet review: 715856
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Abstract: Let $ f$ and $ g$ be polynomials with coefficients in a commutative ring $ A$. Let $ f$ be monic. We show that the resultant of $ f$ and $ g$ equals the norm from $ A[x]{\text{/(}}f{\text{)}}$ to $ A$ of $ g$. As a corollary we deduce that if $ c$ is in $ A$ and also in the ideal generated by $ f$ and $ g$, then the resultant divides $ {c^n}$, where $ n$ is the degree of $ f$.


References [Enhancements On Off] (What's this?)

  • [1] W. D. Brownawell, Some remarks on semi-resultants, Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976) Academic Press, London, 1977, pp. 205–210. MR 0480370
  • [2] L. N. Vaseršteĭn and A. A. Suslin, Serre's problem on projective modules over polynomial rings, and algebraic $ f$-theory, Math. USSR-Izv. 10 (1976), 937-1001. MR 56 #5560.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0715856-2
Keywords: Resultants
Article copyright: © Copyright 1983 American Mathematical Society