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CoGalois groups as metric spaces
Author(s) -
Enochs Edgar,
Estrada Sergio
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410227
Subject(s) - mathematics , orthonormal basis , metric space , topology (electrical circuits) , prime (order theory) , pure mathematics , group (periodic table) , discrete mathematics , combinatorics , physics , quantum mechanics , chemistry , organic chemistry
The coGalois group associated to a torsion free cover of a ℤ‐module are known to have a canonical topology. In this paper we will see that this topology can be deduced by p k ‐roots of elements of coGalois groups over ℤ p ( p is a prime). We shall investigate in the metric associated to this topology and deduce that the coGalois groups are complete and are isomorphic as metric spaces to products of Banach spaces having orthonormal bases over the various rings of p ‐adic integers. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)