On chains associated with abstract key polynomials

Abstract

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-Vaquié chains of $w.$

27 pages