Abstract key polynomials and MacLane-Vaquie chains

  title={Abstract key polynomials and MacLane-Vaquie chains},
  author={Sneha Mavi and Anuj Bishnoi},
  journal={International Journal of Algebra and Computation},
. In this paper, for a valued field ( K,v ) of arbitrary rank and an extension w of v to K ( X ) , a relation between complete sequence of abstract key polynomials, Maclane-Vaqui´e chain and pseudo-convergent sequence of transcendental type is given. 



MacLane–Vaquié chains of valuations on a polynomial ring

Let $(K,v)$ be a valued field. We review some results of MacLane and Vaquie on extensions of $v$ to valuations on the polynomial ring $K[x]$. We introduce certain MacLane-Vaquie chains of residually

MacLane-Vaqui\'e chains and Valuation-Transcendental Extensions

. In this paper, for a valued field ( K, v ) of arbitrary rank and an extension w of v to K ( X ) , we give a connection between complete sets of ABKPs for w and MacLane-Vaqui´e chains of w.

On the implicit constant fields and key polynomials for valuation algebraic extensions

  • Arpan Dutta
  • Mathematics
    Journal of Commutative Algebra
  • 2022
This article is a natural continuation of our previous works [7] and [6]. In this article, we employ similar ideas as in [4] to provide an estimate of IC(K(X)|K, v) when (K(X)|K, v) is a valuation

Of limit key polynomials

Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane–Vaquie key polynomials for valuations μ≤ν and abstract

On MacLane-Vaquié key polynomials

Key polynomials and minimal pairs

Key polynomials over valued fields

  • E. Nart
  • Mathematics
    Publicacions Matemàtiques
  • 2020
Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We

Extension d'une valuation

We want to determine all the extensions of a valuation v of a field K to a cyclic extension L of K, i.e. L = K(x) is the field of rational functions of x or L = K(θ) is the finite separable extension

A construction for absolute values in polynomial rings

||b + c|| < max (||b||, ||c||) then the value l|b|| is called non-archimedean (Ostrowski [17], p. 272). The thus delimited non-archimedean values are of considerable arithmetic interest. They are