Displaying similar documents to “A “class group” obstruction for the equation C y d = F ( x , z ) ”

Prime ideals in semirings.

Gupta, Vishnu, Chaudhari, J.N. (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Hilbert-Speiser number fields and Stickelberger ideals

Humio Ichimura (2009)

Journal de Théorie des Nombres de Bordeaux

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Let p be a prime number. We say that a number field F satisfies the condition ( H p n ′ ) when any abelian extension N / F of exponent dividing p n has a normal integral basis with respect to the ring of p -integers. We also say that F satisfies ( H p ∞ ′ ) when it satisfies ( H p n ′ ) for all n ≥ 1 . It is known that the rationals ℚ satisfy ( H p ∞ ′ ) for all prime numbers p . In this paper, we give a simple condition for a number field F to satisfy ( H p n ′ ) in terms of the ideal class group of K = F ( ζ p n ) and a “Stickelberger ideal” associated to the...

Wilson’s theorem

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 Z to the ring of integers 𝔬 in a number field, to find the product of all invertible elements of a finite quotient of 𝔬 .