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ON COMMUTATIVE NONARCHIMEDEAN BANACH FIELDS
Published Web Locationhttps://doi.org/10.25537/dm.2018v23.171-188
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We study the problem of whether a commutative nonarchimedean Banach ring which is algebraically a field can be topologized by a multiplicative norm. This can fail in general, but it holds for uniform Banach rings under some mild extra conditions. Notably, any perfectoid ring whose underlying ring is a field is a perfectoid field.
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