We describe the additive subgroups of fields which are closed with respect to taking inverses, in particular, with characteristic different from two. Any such subgroup is either a subfield or the kernel of the trace map of a quadratic subextension of the field.
Mattarei, S. (2007). Inverse-closed additive subgroups of fields. ISRAEL JOURNAL OF MATHEMATICS, 159(1), 343-347 [10.1007/s11856-007-0050-6].
Inverse-closed additive subgroups of fields
Mattarei, S
2007
Abstract
We describe the additive subgroups of fields which are closed with respect to taking inverses, in particular, with characteristic different from two. Any such subgroup is either a subfield or the kernel of the trace map of a quadratic subextension of the field.
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