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摘要
It is well known that if f(x) is a monic irreducible polynomial of degree d with coefficients in a complete valued field (K, parallel to), then any monic polynomial of degree d over K which is sufficiently close to f (x) with respect to parallel 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.
- 出版日期2010-2
