Law of inertia for the factorization of cubic polynomials - the imaginary case
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00107142" target="_blank" >RIV/00216224:14310/17:00107142 - isvavai.cz</a>
Alternative codes found
RIV/00216305:26210/17:PU123766
Result on the web
<a href="http://91.203.202.198/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml" target="_blank" >http://91.203.202.198/view/j/ms.2017.67.issue-1/ms-2016-0248/ms-2016-0248.xml</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Law of inertia for the factorization of cubic polynomials - the imaginary case
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GAP201%2F11%2F0276" target="_blank" >GAP201/11/0276: Ideal class groups of algebraic number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Utilitas Mathematica
ISSN
0315-3681
e-ISSN
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Volume of the periodical
103
Issue of the periodical within the volume
June
Country of publishing house
CA - CANADA
Number of pages
11
Pages from-to
99-109
UT code for WoS article
000401308200007
EID of the result in the Scopus database
2-s2.0-85030688530