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The genus class group. I. (English) Zbl 0769.11040

In this paper a direct Hom-language approach is given for the genus class group. The latter is an important new concept which has arisen in the work on additive and multiplicative Galois module structure theory. The intended prospective applications of this paper are on the basic problem of relating modules to arithmetic character invariants.

MSC:

11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
11R65 Class groups and Picard groups of orders
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References:

[1] Fröhlich, A., Locally free modules over arithmetic orders, Crelle274/75 (1975), 112-138. · Zbl 0316.12013
[2] Fröhlich, A., Classgroups and Hermitian modules, Progress in Mathematics48, Birkhäuser1984. · Zbl 0539.12005
[3] Wilson, S.M.J., Galois module structure of the rings of integers in wildly ramified extensions, Ann. Inst. Fourier39 (1989), 529-551. · Zbl 0674.12005
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