An extension of a result of Zaharescu on irreducible polynomials

Khanduja, Sudesh K. ; Ramneek, Khassa (2010) An extension of a result of Zaharescu on irreducible polynomials Indian Journal of Pure and Applied Mathematics, 41 (1). pp. 67-75. ISSN 0019-5588

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Official URL: http://www.springerlink.com/content/48r58835747630...

Related URL: http://dx.doi.org/10.1007/s13226-010-0018-9

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.

Item Type:Article
Source:Copyright of this article belongs to Indian National Science Academy.
Keywords:Valued Fields; Non-archimedean Valued Fields; Irreducible Polynomials
ID Code:69946
Deposited On:19 Nov 2011 10:27
Last Modified:19 Nov 2011 10:27

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