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KLAŠKA, J. SKULA, L.
Original Title
LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE CASE OF DISCRIMINANTS DIVISIBLE BY THREE
Type
journal article in Web of Science
Language
English
Original Abstract
In this paper we extend our recent results concerning the validity of the law of inertia for the factorization of cubic polynomials over the Galois field $F_p$, p being a prime. As the main result, the following theorem will be proved: Let $D\in Z$ and let $C_D$ be the set of all cubic polynomials $x^3 +ax^2 +bx+c\in Z[x]$ with a discriminant equal to $D$. If $D$ is square-free and $3\nmid h(-3D)$ where $h(-3D)$ is the class number of $Q(\sqrt(-3D))$, then all cubic polynomials in $C_D$ have the same type of factorization over any Galois field $F_p$ where $p$ is a prime, $p > 3$.
Keywords
cubic polynomial, factorization, Galois field
Authors
Released
24. 11. 2016
Publisher
Slovenská akademie věd
Location
SK
ISBN
0139-9918
Periodical
Mathematica Slovaca
Year of study
66
Number
4
State
Slovak Republic
Pages from
1019
Pages to
1027
Pages count
9
BibTex
@article{BUT129973, author="Jiří {Klaška} and Ladislav {Skula}", title="LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE CASE OF DISCRIMINANTS DIVISIBLE BY THREE", journal="Mathematica Slovaca", year="2016", volume="66", number="4", pages="1019--1027", doi="10.1515/ms-2015-0199", issn="0139-9918" }