On resultants

Gerald Myerson

doi:10.1090/S0002-9939-1983-0715856-2

On resultants

Gerald Myerson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let ƒ and g be polynomials with coefficients in a commutative ring A. Let ƒ be monic. We show that the resultant of/and g equals the norm from A[x] ƒ (ƒ) to A of g. As a corollary we deduce that if c is in A and also in the ideal generated by ƒ and g, then the resultant divides cⁿ, where n is the degree of ƒ.

Original language	English
Pages (from-to)	419-420
Number of pages	2
Journal	Proceedings of the American Mathematical Society
Volume	89
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1983-0715856-2
Publication status	Published - 1983
Externally published	Yes

Keywords

Resultants

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10.1090/S0002-9939-1983-0715856-2

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title = "On resultants",

abstract = "Let ƒ and g be polynomials with coefficients in a commutative ring A. Let ƒ be monic. We show that the resultant of/and g equals the norm from A[x] ƒ (ƒ) to A of g. As a corollary we deduce that if c is in A and also in the ideal generated by ƒ and g, then the resultant divides cn, where n is the degree of ƒ.",

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AU - Myerson, Gerald

PY - 1983

Y1 - 1983

N2 - Let ƒ and g be polynomials with coefficients in a commutative ring A. Let ƒ be monic. We show that the resultant of/and g equals the norm from A[x] ƒ (ƒ) to A of g. As a corollary we deduce that if c is in A and also in the ideal generated by ƒ and g, then the resultant divides cn, where n is the degree of ƒ.

AB - Let ƒ and g be polynomials with coefficients in a commutative ring A. Let ƒ be monic. We show that the resultant of/and g equals the norm from A[x] ƒ (ƒ) to A of g. As a corollary we deduce that if c is in A and also in the ideal generated by ƒ and g, then the resultant divides cn, where n is the degree of ƒ.

KW - Resultants

UR - http://www.scopus.com/inward/record.url?scp=84966240166&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1983-0715856-2

DO - 10.1090/S0002-9939-1983-0715856-2

M3 - Article

AN - SCOPUS:84966240166

VL - 89

SP - 419

EP - 420

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -

On resultants

Abstract

Keywords

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