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- W4288261608 abstract "Let $(K,nu)$ be an arbitrary-rank valued field, $R_nu$ its valuation ring, $K(alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $fin R_nu[X]$. We give necessary and sufficient conditions for $R_nu[alpha]$ to be integrally closed. We further characterize the integral closedness of $R_nu[alpha]$ based on information about the valuations on $K(alpha)$ extending $nu$. Our results enhance and generalize some existing results in the relevant literature. Some applications and examples are also given." @default.
- W4288261608 created "2022-07-28" @default.
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- W4288261608 date "2019-08-17" @default.
- W4288261608 modified "2023-09-27" @default.
- W4288261608 title "A Dedekind's Criterion over Valued Fields" @default.
- W4288261608 doi "https://doi.org/10.48550/arxiv.1908.06365" @default.
- W4288261608 hasPublicationYear "2019" @default.
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