Minimal pairs, minimal fields and implicit constant fields

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dc.contributor.authorDutta, Arpan
dc.date.accessioned2023-08-24T11:01:27Z
dc.date.available2023-08-24T11:01:27Z
dc.date.issued2021
dc.descriptionOnly IISER Mohali authors are available in the record.en_US
dc.description.abstractMinimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu [3], [4], [5] to study residue transcendental extensions. In this paper we obtain analogous results in the value transcendental case. We introduce the notion of minimal fields of definition for valuation transcendental extensions and show that they share some common ramification theoretic properties. The connection between minimal fields of definition and implicit constant fields is also investigated. Further, we explore the relationship between valuation transcendental extensions and pseudo-Cauchy sequences.en_US
dc.identifier.citationJournal of Algebra, 588, 479–514.en_US
dc.identifier.urihttps://doi.org/10.1016/j.jalgebra.2021.09.008
dc.identifier.urihttp://hdl.handle.net/123456789/5168
dc.language.isoen_USen_US
dc.publisherElsevieren_US
dc.subjectValuationen_US
dc.subjectMinimal pairsen_US
dc.subjectKey polynomialsen_US
dc.subjectPseudo-Cauchy sequencesen_US
dc.subjectValuation transcendental extensionsen_US
dc.titleMinimal pairs, minimal fields and implicit constant fieldsen_US
dc.typeArticleen_US

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