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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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