Valuations, Valued Field and Construction of Valuation over the Rings

Abstract

The definition of the valuation is studied on the finite structures. Since the ideals can be classified in particular, the finite chain rings are dealt with as a definition set. With these ideals, the maximal ideals of the valuation rings are matched. In addition, the unit groups of the writing valuations and the unit elements of the ring were compared.

Keywords: Valuations, Valuation Theory, Valued Fields, Valuation Ring.