Publication result detail

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE CASE OF DISCRIMINANTS DIVISIBLE BY THREE

KLAŠKA, J. SKULA, L.

Original Title

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE CASE OF DISCRIMINANTS DIVISIBLE BY THREE

English Title

LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE CASE OF DISCRIMINANTS DIVISIBLE BY THREE

Type

WoS Article

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, $p > 3$.

English 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

Key words in English

cubic polynomial, factorization, Galois field

Authors

KLAŠKA, J. SKULA, L.

RIV year

2017

Released

24.11.2016

Publisher

Slovenská akademie věd

Location

SK

ISBN

0139-9918

Periodical

Mathematica Slovaca

Volume

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"
}