Compositions of consistent systems of rank one discrete valuation rings

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dc.creatorHeinzer, William J.
dc.creatorRatliff Jr., Louis J.
dc.creatorRush, David E.
dc.date2008-09-26
dc.date.accessioned2026-07-07T10:05:39Z
dc.date.available2026-07-07T10:05:39Z
dc.descriptionLet V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the number of extensions of V to a valuation ring W on L, (ii) the residue degree of each W over V, and (iii) the ramification degree of each W over V. Given a finite set of DVRs on F, an m-consistent system is a family of sets enumerating what is theoretically possible for the above invariants of each V in the set. The m-consistent system is realizable if there exists a finite separable extension field L/F that gives for each V the listed invariants. We investigate the realizability of m-consistent systems.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/0809.4525
dc.identifierhttp://arxiv.org/abs/0809.4525
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170070
dc.subjectCommutative Algebra
dc.subject13F05
dc.titleCompositions of consistent systems of rank one discrete valuation rings
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