Polynomials with Special Regard to Reducibility

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Cambridge University Press, Apr 27, 2000 - Mathematics
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This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.

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Lacunary polynomials over an arbitrary field
Polynomials over an algebraically closed field
Polynomials over a finitely generated field
Polynomials over a number field
Polynomials over a Kroneckerian field

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Page 1 - prime if it is not the composition of two polynomials of lower degree and proved the two main results: (i) In every representation of a polynomial as the composition of prime polynomials the number of factors is the same and their degrees coincide up to a permutation. (ii) If
Page 11 - ord , a is the highest power to which a prime element p of a unique factorization domain or a prime ideal p of a Dedekind domain divides an element a of this domain.

References to this book

Cogalois Theory
Toma Albu
Limited preview - 2002
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