Polynomials with a common composite

Robert M. Beals; Joseph L. Wetherell; Michael E. Zieve

doi:10.1007/s11856-009-0105-y

Polynomials with a common composite

Robert M. Beals, Joseph L. Wetherell, Michael E. Zieve

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

5 Scopus citations

Abstract

Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.

Original language	English (US)
Pages (from-to)	93-117
Number of pages	25
Journal	Israel Journal of Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.1007/s11856-009-0105-y
State	Published - Nov 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s11856-009-0105-y

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title = "Polynomials with a common composite",

abstract = "Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.",

author = "Beals, {Robert M.} and Wetherell, {Joseph L.} and Zieve, {Michael E.}",

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AU - Beals, Robert M.

AU - Wetherell, Joseph L.

AU - Zieve, Michael E.

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Y1 - 2009/11

N2 - Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.

AB - Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.

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DO - 10.1007/s11856-009-0105-y

M3 - Article

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EP - 117

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -

Polynomials with a common composite

Abstract

All Science Journal Classification (ASJC) codes

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