Manis, Merle Eugene2023-09-112023-09-111966-06https://hdl.handle.net/1794/2888582 pagesThe purpose of this paper is to extend some results from the theory of valuations on a field to an arbitrary commutative ring with identity. The results obtained are well known when interpreted in the context of a field and comprise only a bare introduction -to the theory for fields, however, the modified proofs give some added insight even in this case.enCreative Commons BY-NC-ND 4.0-USinverse propertyapproximation theorumsGalois extensionsThesis / Dissertation