On ramification index of composition of complete discrete valuation fields

Autor: Pasupulati Sunil Kumar
Rok vydání: 2020
Předmět:
Zdroj: Proceedings - Mathematical Sciences. 130
ISSN: 0973-7685
0253-4142
DOI: 10.1007/s12044-020-00572-w
Popis: For an extension L/K of discrete valuation fields, let $$e_{L/K}$$ , $${\mathfrak {O}}_{L}$$ denote the ramification index and valuation ring of L/K respectively. Let K be a complete discrete valuation field and $$L_1/K$$ , $$L_2/K$$ be finite linearly disjoint extensions over K. We show that if $${\mathfrak {O}}_{L_1L_2} ={\mathfrak {O}}_{L_1}{\mathfrak {O}}_{L_2}$$ or $$\mathrm {gcd}(e_{L_1/K}, e_{L_2/K}) =1$$ , and one of the residue fields $$l_1/k,$$ $$l_2/k$$ is separable, then $$e_{L_1L_2/L_1} =e_{L_2/K}.$$ The analogous results for the residue degrees are also true.
Databáze: OpenAIRE
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