About the kernel of the augmentation of finitely generated Z-modules
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AbstractLet M be a free finitely generated Z-module with basis B and ΔM the kernel of the homomorphism M→Z which maps B to 1. A basis of ΔM 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 ΔN = (ΔM + R) / R. We compute the index [N:ΔN] and construct bases of ΔN 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.
CitationConrad, M., (2000) 'About the Kernel of the Augmentation of finitely generated Z-modules', Mathematical Communications 5, pp. 61-66
PublisherUniversity of Osijek
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