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A Generalization of the Eisenstein–Dumas–Schönemann Irreducibility Criterion

Part of: General field theory Algebraic number theory: global fields Topological fields

Published online by Cambridge University Press:  31 January 2017

Bablesh Jhorar  and
Sudesh K. Khanduja
Bablesh Jhorar
Affiliation:
Department of Mathematics, Panjab University, Chandigarh-160014, India (bableshtarar@gmail.com)
Sudesh K. Khanduja*
Affiliation:
Indian Institute of Science Education and Research Mohali, Sector 81, SAS Nagar-140306, Punjab, India (skhanduja@iisermohali.ac.in)
*
*Corresponding author.
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Abstract

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.

Keywords

Eisenstein criterionirreducibilityvalued fields

MSC classification

Secondary: 12E05: Polynomials (irreducibility, etc.) 11R09: Polynomials (irreducibility, etc.) 12J10: Valued fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 4 , November 2017 , pp. 937 - 945
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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