On Newton polygons techniques and factorization of polynomials over Henselian fields

El Fadil Lhoussain

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On Newton polygons techniques and factorization of polynomials over Henselian fields

机译：On Newton polygons techniques and factorization of polynomials over Henselian fields

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摘要

Let (K, nu) be a valued field, where nu is a rank-one discrete valuation, with valuation ring R. The goal of this paper is to investigate some basic concepts of Newton polygon techniques of a monic polynomial f (x) is an element of R[x]; namely, theorem of the product, of the polygon, and of the residual polynomial, in such way that improves that given in [D. Cohen, A. Movahhedi and A. Salinier, Factorization over local fields and the irreducibility of generalized difference polynomials, Mathematika 47 (2000) 173-196] and generalizes that given in [J. Guardia, J. Montes and E. Nart, Newton polygons of higher order in algebraic number theory, Trans. Amer. Math. Soc. 384(1) (2012) 361-416] to any rank-one valued field.

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《Journal of algebra and its applications》 |2020年第10期|共9页
作者
El Fadil Lhoussain;
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作者单位

Sidi Mohamed ben Abdellah Univ, Fac Sci Dhar El Mahraz, Fes, Morocco;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
Valued fields; Henselization; Newton polygon; theorem of the polygon; theorem of the residual polynomial; prime ideal factorization;

On Newton polygons techniques and factorization of polynomials over Henselian fields

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