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

4 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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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.",

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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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Polynomials with a common composite

Abstract

All Science Journal Classification (ASJC) codes

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