In this paper we present a characterization for the defect of simple algebraic extensions of
valued fields. This characterization generalizes the known result for the henselian case …

Assume that $(L, v) $ is a finite Galois extension of a valued field $(K, v) $. We give an
explicit construction of the valuation ring $\cO_L $ of $ L $ as an $\cO_K $-algebra, and an …

In this paper we present different ways to parametrize subsets of the space of valuations on
K [x] extending a given valuation on K. We discuss the methods using pseudo-Cauchy …

For important cases of algebraic extensions of valued fields, we develop presentations of the
associated K\" ahler differentials of the extensions of their valuation rings. We compute their …

In this paper we present a characterization for the defect of a simple algebraic extensions of
valued fields. This characterization generalizes the known result for the henselian case …