Dense subfields of henselian fields, and integer parts

Details Dense subfields of henselian fields, and integer parts Dense subfields of henselian fields, and integer parts

2010-03-29

arxiv.org/abs/1003.5681v1

Lecture Notes in Logic 26 (2006), 204-226

Mathematics

Commutative Algebra

23 pages; Proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic, held October 18-22, 2003.

Scientific paper

We show that every henselian valued field $L$ of residue characteristic 0 admits a proper subfield $K$ which is dense in $L$. We present conditions under which this can be taken such that $L|K$ is transcendental and $K$ is henselian. These results are of interest for the investigation of integer parts of ordered fields. We present examples of real closed fields which are larger than the quotient fields of all their integer parts. Finally, we give rather simple examples of ordered fields that do not admit any integer part and of valued fields that do not admit any subring which is an additive complement of the valuation ring.

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