Localization in a principal right ideal domain
Abstract: Let be a principal right ideal domain with right -chain , and let be the associated chain of quotient rings of . The local skew degree of is defined to be the least ordinal such that is a local ring. The main result states that for each is a local ring; equivalently, has a unique -prime for .
Keywords: PRI domain, -chain, primes, infinite primes, localization
Article copyright: © Copyright 1972 American Mathematical Society