Bounds for the multiplicities of the irreducible factors of a multivariate polynomial

A. I. Bonciocat; Nicolae C. Bonciocat; A. Zaharescu

doi:10.1080/00927871003645425

Bounds for the multiplicities of the irreducible factors of a multivariate polynomial

A. I. Bonciocat, Nicolae C. Bonciocat, A. Zaharescu

Mathematics

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

Abstract

We provide explicit upper bounds for the multiplicities of the irreducible factors for some classes of polynomials in two variables X, Y over a field K, regarded as polynomials in Y with coefficients in K[X] whose degrees satisfy certain inequalities. We then obtain similar results for polynomials in an arbitrary number of variables over K.

Original language	English (US)
Pages (from-to)	1131-1138
Number of pages	8
Journal	Communications in Algebra
Volume	39
Issue number	3
DOIs	https://doi.org/10.1080/00927871003645425
State	Published - Mar 2011

Keywords

Multiplicity of an irreducible factor
Square-free polynomial

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927871003645425

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abstract = "We provide explicit upper bounds for the multiplicities of the irreducible factors for some classes of polynomials in two variables X, Y over a field K, regarded as polynomials in Y with coefficients in K[X] whose degrees satisfy certain inequalities. We then obtain similar results for polynomials in an arbitrary number of variables over K.",

keywords = "Multiplicity of an irreducible factor, Square-free polynomial",

author = "Bonciocat, {A. I.} and Bonciocat, {Nicolae C.} and A. Zaharescu",

note = "Funding Information: This research was partially supported by the CNCSIS grant ID-PCE 443/2008, code 1190, of the Romanian Ministry of Education and Research.",

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AU - Bonciocat, A. I.

AU - Bonciocat, Nicolae C.

AU - Zaharescu, A.

N1 - Funding Information: This research was partially supported by the CNCSIS grant ID-PCE 443/2008, code 1190, of the Romanian Ministry of Education and Research.

PY - 2011/3

Y1 - 2011/3

N2 - We provide explicit upper bounds for the multiplicities of the irreducible factors for some classes of polynomials in two variables X, Y over a field K, regarded as polynomials in Y with coefficients in K[X] whose degrees satisfy certain inequalities. We then obtain similar results for polynomials in an arbitrary number of variables over K.

AB - We provide explicit upper bounds for the multiplicities of the irreducible factors for some classes of polynomials in two variables X, Y over a field K, regarded as polynomials in Y with coefficients in K[X] whose degrees satisfy certain inequalities. We then obtain similar results for polynomials in an arbitrary number of variables over K.

KW - Multiplicity of an irreducible factor

KW - Square-free polynomial

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Bounds for the multiplicities of the irreducible factors of a multivariate polynomial

Abstract

Keywords

ASJC Scopus subject areas

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