VALUATIONS ON VECTOR SPACES AS A GENERALIZATION OF VALUATIONS ON FIELDS - EFRINITA IRWAN (30113010), SRI
This dissertation deals with valuations on vector spaces as a generalization of valuations on fields. The resulting contribution is formulation the concept of valuations on vector spaces as a generalization of valuations on fields. The main result of the dissertation is an interrelation between valuation modules and valuations on vector spaces. This result obtained as a generalization of the similar study in ring theory. This study is restricted to the class of torsion-free reduced modules. In the next discussion, it is shown that it can be constructed a topology on a reduced valuation module using the corresponding valuation on the module. As a result, every reduced valuation module is a topological module. Further, we use the results to study the completion of valuation modules. Particularly, investigated the completion of torsion-free reduced modules over discrete valuation rings.