INITIAL RAMIFICATION INDEX OF NONINVARIANT VALUATIONS ON FINITE DIMENSIONAL DIVISION ALGEBRAS
Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation ri...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1997-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31257_15f75ef1d10234576e559849154d710f.pdf |
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| Summary: | Let D be a division ring with centre K and dim, D< ? a valuation on K and v a
noninvariant extension of ? to D. We define the initial ramfication index of v over
?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A .
If B= A , it is shown that the following conditions are equivalent: (i) B is a finite A-module, (ii) B is a free A-module, (iii) [B/mB: A/m] = [D: k], (iv) e(v / ?) f(v / ?)= [D: K] and ? (v / ?)= e(v / ?). It is also proved that if ? (v/ ?) = e(v/ ?), and any of (i) - (iv) holds, then v is invariant |
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| ISSN: | 1016-1104 2345-6914 |