Law of inertia for the factorization of cubic polynomials - the imaginary case

KLAŠKA, Jiří and Ladislav SKULA. Law of inertia for the factorization of cubic polynomials - the imaginary case. Utilitas Mathematica. Winnipeg, Kanada: Util Math Publ Inc, 2017, vol. 103, June, p. 99-109. ISSN 0315-3681.

Basic information

• Original name: Law of inertia for the factorization of cubic polynomials - the imaginary case
• Authors: KLAŠKA, Jiří (203 Czech Republic, guarantor) and Ladislav SKULA (203 Czech Republic, belonging to the institution).
• Edition: Utilitas Mathematica, Winnipeg, Kanada, Util Math Publ Inc, 2017, 0315-3681.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Canada
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.267
• RIV identification code: RIV/00216224:14310/17:00107142
• Organization unit: Faculty of Science
• UT WoS: 000401308200007
• Keywords in English: cubic polynomial; type of factorization; discriminant
• Tags: NZ, rivok
• Tags: International impact, Reviewed

Abstract

Let D be a square-free positive integer not divisible by 3 such that the class number h(-3D) of Q((-3D)^(1/2)) is also not divisible by 3. We prove that all cubic polynomials f (x) = x^3 + ax^2 + bx + c in Z[x] with a discriminant D have the same type of factorization over any Galois field F_p, where p is a prime bigger than 3. Moreover, we show that any polynomial f(x) with such a discriminant D has a rational integer root. A complete discussion of the case D = 0 is also included.

Links

• GAP201/11/0276, research and development project: Name: Grupy tříd ideálů algebraických číselných těles

Investor: Czech Science Foundation