About the kernel of the augmentation of finitely generated Z - modules
نویسندگان
چکیده
Let M be a free finitely generated Z-module with basis B and ∆M the kernel of the homomorphism M → Z which maps B to 1. A basis of ∆M can be easily constructed from the basis B of M . Let further R be a submodule of M such that N = M/R is free. The subject of investigation is the module ∆N = (∆M + R)/R. We compute the index [N : ∆N ] and construct bases of ∆N with the help of a basis of N . Finally, the results are applied to a special class of modules which is connected with the group of cyclotomic units.
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