• Corpus ID: 248157592

On chains associated with abstract key polynomials

  title={On chains associated with abstract key polynomials},
  author={Sneha Mavi and Anuj Bishnoi},
. In this paper, for a henselian valued field ( K,v ) of arbitrary rank and an extension w of v to K ( X ) , we use abstract key polynomials for w to give a connection between complete sets, saturated distinguished chains and Okutsu frames. Further, for a valued field ( K,v ) , we also obtain a close connection between complete set of ABKPs for w and Maclane-Vaqui´e chains of w. 



Defectless polynomials over henselian fields and inductive valuations

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

Abstract Key Polynomials and Distinguished Pairs

For a henselian valued field (K,v) of arbitrary rank and an extension w of v to K(X), abstract key polynomials for w are used to obtain distinguished pairs and saturated distinguished chains.

Key polynomials and distinguished pairs

Abstract In this article, we establish a connection between key polynomials over a residually transcendental prolongation of a henselian valuation on a field K and distinguished pairs. We also derive

On truncations of valuations

Of limit key polynomials

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On common extensions of valued fields

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

On the structure of the irreducible polynomials over local fields

The paper is concerned with the structure of irreducible polynomials in one variable over a local field (K, v). The main achievement is the definition of a system P(ƒ) of invariant factors for each