Residual ideals of MacLane valuations
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Let K be a field equipped with a discrete valuation v. In a pioneering work, MacLane determined all valuations on K(x) extending v. His work was recently reviewed and generalized by Vaqui´e, by using the graded algebra of a valuation. We extend Vaqui´e’s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of the theory. As a consequence, we determine the structure of the graded algebra of the discrete valuations on K(x) and we show how these valuations may be used to parameterize irreducible polynomials over local fields up to Okutsu equivalence
CitationFernández, J. [et al.]. Residual ideals of MacLane valuations. "Journal of algebra", 2015, vol. 427, p. 30-75.