Square-free criteria for polynomials using no derivatives

E. Alkan; A. I. Bonciocat; N. C. Bonciocat; A. Zaharescu

doi:10.1090/S0002-9939-06-08526-1

Square-free criteria for polynomials using no derivatives

E. Alkan, A. I. Bonciocat, N. C. Bonciocat, A. Zaharescu

Mathematics

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

Abstract

We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce squarefree criteria for polynomials in several variables.

Original language	English (US)
Pages (from-to)	677-687
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	135
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-06-08526-1
State	Published - Mar 2007

Keywords

Frobenius map
Primitive polynomials
Resultants
Square-free criteria

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Online availability

10.1090/S0002-9939-06-08526-1

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title = "Square-free criteria for polynomials using no derivatives",

abstract = "We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce squarefree criteria for polynomials in several variables.",

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AU - Bonciocat, A. I.

AU - Bonciocat, N. C.

AU - Zaharescu, A.

PY - 2007/3

Y1 - 2007/3

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KW - Primitive polynomials

KW - Resultants

KW - Square-free criteria

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Square-free criteria for polynomials using no derivatives

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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