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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Effective determination of the decomposition of the rational primes in a cubic field


Authors: Pascual Llorente and Enric Nart
Journal: Proc. Amer. Math. Soc. 87 (1983), 579-585
MSC: Primary 12A30; Secondary 12A50
MathSciNet review: 687621
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Abstract: The decomposition of the rational primes in a cubic field $ K$ is determined in terms of the coefficients of a defining polynomial of $ K$. As a consequence, the discriminant $ D$ of $ K$ is straightforwardly computed and the cubic fields with index $ i(K) = 2$ are easily characterized.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687621-6
PII: S 0002-9939(1983)0687621-6
Keywords: Cubic field, ramification, discriminant, index of a number field
Article copyright: © Copyright 1983 American Mathematical Society