On residual algebraic torsion extensions of a valuation of a field K to K x1 xn

İngilizce (OpenAlex)

Let v be a valuation of a field K with a value group and a residue field , w be an extension of v to . Then w is called a residual algebraic torsion extension of v to if is an algebraic extension and is a torsion group. In this paper, a residual algebraic torsion extension of v to is described and its certain properties are investigated. Also, the existence of a residual algebraic torsion extension of a valuation on K to with given residue field and value group is studied. MSC:12J10, 12J20, 12F20.