An extension of a result of Zaharescu on irreducible polynomials

Sudesh K. Khanduja () and Ramneek Khassa ()
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Sudesh K. Khanduja: Panjab University
Ramneek Khassa: Panjab University

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 67-75

Abstract: Abstract It is well known that if f(x) is a monic irreducible polynomial of degree d with coefficients in a complete valued field (K, ‖), then any monic polynomial of degree d over K which is sufficiently close to f(x) with respect to ‖ is also irreducible over K. In 2004, Zaharescu proved a similar result applicable to separable, irreducible polynomials over valued fields which are not necessarily complete. In this paper, the authors extend Zaharescu’s result to all irreducible polynomials without assuming separability.

Keywords: Valued fields; non-Archimedean valued fields; irreducible polynomials (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0018-9

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