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Stickelberger subideals related to Kummer type congruences. (English) Zbl 0956.11009
Summary: A new type of the Kummer system of congruences is considered and some equivalent systems are discussed by using a polynomial identity. Further we define a special Stickelberger subideal in a certain group ring and transfer the Fueter type system into the group ring. Afterwards, by evaluating the determinant of a special matrix we deduce the index formula between the group ring, and the Stickelberger subideal in terms of the relative class number of the \(l\)th cyclotomic field (where \(l\geq 5\) is an odd prime).
MSC:
11D41 Higher degree equations; Fermat’s equation
11B68 Bernoulli and Euler numbers and polynomials
11R54 Other algebras and orders, and their zeta and \(L\)-functions
11R29 Class numbers, class groups, discriminants
11R18 Cyclotomic extensions
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References:
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