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 obtain distinguished pairs and saturated distinguished chains.

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.

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ABSTRACT. Let v be a valuation of a field K having value group Z. It is known that a polynomial x n

Abstract. Let v be a Henselian Krull valuation of a field K. In this paper, the authors give some necessary and sufficient conditions for a finite simple extension of (K, v) to be defectless. Various characterizations of algebraically maximal valued fields are also given which lead to a new proof of a result proved