Abstract
In this chapter we describe a technique for deciding whether a given polynomial in ℤp[x], p an odd prime, has an odd or an even number of distinct irreducible factors. The theorem is this:Stickelberger“s Theorem. Let p be an odd prime, f a monk polynomial of degree d with coefficients in ℤp[x], without repeated roots in any splitting field. Let r be the number of irreducible factors of f in ℤp[x]. Then r≡d (mod 2) iff the discriminant D(f) is a square in ℤp. .
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© 1979 Springer-Verlag New York Inc.
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Childs, L. (1979). The Discriminant and Stickelberger’s Theorem. In: A Concrete Introduction to Higher Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0065-6_43
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DOI: https://doi.org/10.1007/978-1-4684-0065-6_43
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0067-0
Online ISBN: 978-1-4684-0065-6
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