On resultants
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- by Gerald Myerson
- Proc. Amer. Math. Soc. 89 (1983), 419-420
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715856-2
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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
- 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 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.
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- 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