Module structure of integers in metacyclic extensions
James Carter (1998)
Colloquium Mathematicae
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James Carter (1998)
Colloquium Mathematicae
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Humio Ichimura (2009)
Journal de Théorie des Nombres de Bordeaux
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Let be a prime number. We say that a number field satisfies the condition when any abelian extension of exponent dividing has a normal integral basis with respect to the ring of -integers. We also say that satisfies when it satisfies for all . It is known that the rationals satisfy for all prime numbers . In this paper, we give a simple condition for a number field to satisfy in terms of the ideal class group of and a “Stickelberger ideal” associated to the...
Chandan Singh Dalawat (2009)
Journal de Théorie des Nombres de Bordeaux
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We show how K. Hensel could have extended Wilson’s theorem from to the ring of integers in a number field, to find the product of all invertible elements of a finite quotient of .
Ferrero, Miguel, Steffenon, Rogério Ricardo (2004)
Beiträge zur Algebra und Geometrie
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Supriya Pisolkar (2009)
Journal de Théorie des Nombres de Bordeaux
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We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about -primary units. We also prove a similar statement about the absolute norms of -primary units, for all primes .
J. Wójcik (1996)
Colloquium Mathematicae
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Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2011)
Formalized Mathematics
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In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.