Publications of the Research Institute for Mathematical Sciences


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Volume 50, Issue 2, 2014, pp. 269–285
DOI: 10.4171/PRIMS/133

Published online: 2014-06-11

On the Field-theoreticity of Homomorphisms between the Multiplicative Groups of Number Fields

Yuichiro Hoshi[1]

(1) Kyoto University, Japan

We discuss the eld-theoreticity of homomorphisms between the multiplicative groups of number fi elds. We prove that, for instance, for a given isomorphism between the multiplicative groups of number fields, either the isomorphism or its multiplicative inverse arises from an isomorphism of fields if and only if the given isomorphism is SPU-preserving (i.e., roughly speaking, preserves the subgroups of principal units with respect to various nonarchimedean primes).

Keywords: number field, multiplicative group, field-theoreticity, PU-preserving homomorphism

Hoshi Yuichiro: On the Field-theoreticity of Homomorphisms between the Multiplicative Groups of Number Fields. Publ. Res. Inst. Math. Sci. 50 (2014), 269-285. doi: 10.4171/PRIMS/133