On Eisenstein–Dumas and Generalized Schönemann Polynomials

Bishnoi, Anuj; Khanduja, Sudesh K.

doi:10.1080/00927870903164669

Cited by 8 publications

(1 citation statement)

References 6 publications

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“…More recent generalizations of the irreducibility criteria of Schönemann and Schönemann-Eisenstein, and results related to the study of generalized Schönemann and Eisenstein-Dumas polynomials have been obtained by Panaitopol andŞtefȃnescu [31], Khanduja and Saha [22], Brown [3], Bush and Hajir [4], Bishnoi and Khanduja [2], Khanduja and Khassa [21], and Weintraub [36].…”

Section: Irreducibility Criteria 3103mentioning

confidence: 99%

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Bonciocat

2015

Communications in Algebra

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The famous irreducibility criteria of Schönemann-Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this paper, we will use some results and ideas of Dumas to provide several irreducibility criteria of Schönemann-Eisenstein-Dumas-type for polynomials with integer coefficients, criteria that are given by some divisibility conditions for their coefficients with respect to arbitrarily many prime numbers. A special attention will be paid to those irreducibility criteria that require information on the divisibility of the coefficients by two distinct prime numbers.

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Section: Irreducibility Criteria 3103mentioning

confidence: 99%

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Bonciocat

2015

Communications in Algebra

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Some Extensions and Applications of the Eisenstein Irreducibility Criterion

Bishnoi

Khanduja

2010

Quadratic Forms, Linear Algebraic Groups, and Cohomology

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A Generalization of the Eisenstein–Dumas–Schönemann Irreducibility Criterion

Jhorar¹,

Khanduja²

2017

Proceedings of the Edinburgh Mathematical Society

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In 2013, Weintraub gave a generalization of the classical Eisenstein irreducibility criterion in an attempt to correct a false claim made by Eisenstein. Using a different approach, we prove Weintraub's result with a weaker hypothesis in a more general setup that leads to an extension of the generalized Schönemann irreducibility criterion for polynomials with coefficients in arbitrary valued fields.

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On Eisenstein–Dumas and Generalized Schönemann Polynomials

Abstract: ABSTRACT. Let v be a valuation of a field K having value group Z. It is known that a polynomial x n

Cited by 8 publications

References 6 publications

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Some Extensions and Applications of the Eisenstein Irreducibility Criterion

A Generalization of the Eisenstein–Dumas–Schönemann Irreducibility Criterion

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