Detailed Information on Publication Record
2017
Law of inertia for the factorization of cubic polynomials - the imaginary case
KLAŠKA, Jiří and Ladislav SKULABasic 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
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Canada
Confidentiality degree
není předmětem státního či obchodního tajemství
References:
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
International impact, Reviewed
Změněno: 9/4/2020 14:41, Mgr. Marie Šípková, DiS.
Abstract
V originále
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 |
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