Valuations defined by Ostrowski nets |
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Authors: | David Mathews Jo-Ann Cohen |
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Institution: | Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA |
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Abstract: | Ostrowski proved that if v is a valuation on an algebraically closed field F and if w is a valuation extending v to the field F (x) of rational functions over F, then w is defined by a transcendental pseudo-convergent net (that is, an Ostrowski net) or w is a Rella extension of v centered about x ? c for some c in F. In this paper, valuations on the field of rational functions over an arbitrary field determined by Ostrowski nets, along with the topologies they generate, are investigated. |
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