Detail publikace

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

KLAŠKA, J. SKULA, L.

Anglický název

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

Typ

Článek WoS

Jazyk

en

Originální abstrakt

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, $p > 3$.

Klíčová slova anglicky

cubic polynomial, factorization, Galois field

Vydáno

2016-11-24

Nakladatel

Slovenská akademie věd

Místo

SK

ISSN

0139-9918

Časopis

Mathematica Slovaca

Ročník

66

Číslo

4

Strany od–do

1019–1027

Počet stran

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"
}