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• W2963458632 abstract "Let (K,v) be a discrete valued field and let x be an indeterminate. In 1936, MacLane determined all valuations on K(x) extending v. His work has been reviewed and generalized by Vaquié, by using the graded algebra of a valuation. We extend Vaquié's approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials having a key role in the computational applications of the theory. This enables us to determine the structure of the graded algebra of the discrete valuations on K(x). Also, let P be the set of monic irreducible polynomials with coefficients in the completion Ov of the valuation ring of v. The constructive methods of the paper yield a canonical bijection P/≈→M, between the set of Okutsu equivalence classes of prime polynomials and a certain MacLane space M, whose points may be described in terms of discrete parameters associated with valuations on K(x)." @default.
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• W2963458632 date "2015-04-01" @default.
• W2963458632 modified "2023-10-16" @default.
• W2963458632 title "Residual ideals of MacLane valuations" @default.
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• W2963458632 doi "https://doi.org/10.1016/j.jalgebra.2014.12.022" @default.
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