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Preprint Number 1567

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1567. Peter Sinclair
Immediately algebraically closed fields
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Submission date: 15 February 2019

Abstract:

We consider two overlapping classes of fields, IAC and VAC, which are defined using valuation theory but which do not involve a distinguished valuation. Rather, each class is defined by a condition that quantifies over all possible valuations on the field. In his thesis, Hong asked whether these two classes are equal (Hong, 2013, Question 5.6.8). In this paper, we give an example that negatively answers Hong's question. We also explore several situations in which the equivalence holds with an additional assumption, including the case where every K'≡ K is IAC.

Mathematics Subject Classification: 12J10, 12J25, 03C60, 12L12

Keywords and phrases:

Full text arXiv 1902.05830: pdf, ps.


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