Noncommutative Valuation Rings


Elbert_M. Pirtle


Noncommutative valuation rings are duo rings: Every right ideal is a left ideal and conversely. Properties of noncommutative valuation rings are compared to those of commutative valuation rings. Noncommutative valuatiun rings are integrally closed. A noncommutative valuation rings has all the properties of a commutative valuation ring if all its prime ideals are invariant.