• On ramification index of composition of complete discrete valuation fields

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    • Keywords


      Complete discrete valuation fields; ramification indices; linearly disjoint extensions.

    • Abstract


      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 $\mathfrak{O}_{L_1L_2}=\mathfrak{O}_{L_1}\mathfrak{O}_{L2}$ or 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.

    • Author Affiliations



      1. Indian Institute of Science Education and Research, Thiruvananthapuram 695 551, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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