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Let v be a valuation of a field K with a value group GvOpen image in new window and a residue field kvOpen image in new window, w be an extension of v to K(x)Open image in new window. Then w is called a residual algebraic torsion extension of v to K(x)Open image in new window if kw/kvOpen image in new window is an algebraic extension and Gw/GvOpen image in new window is a torsion group. In this paper, a residual algebraic torsion extension of v to K(x1,…,xn)Open image in new window is described and its certain properties are investigated. Also, the existence of a residual algebraic torsion extension of a valuation on K to K(x1,…,xn)Open image in new window with given residue field and value group is studied.

On residual algebraic torsion extensions of a valuation of a field K to K ( x 1 , … , x n )