Some rings of interest in the study of places

Abstract

The rings studied in this paper were first constructed in connexion with the problem (Proposition 1) of extending a place from an integral domain to its field of fractions. They provide (Proposition 3) a series of examples of places not so extendable, generalizing an example implicit in the work of Samuel(3); and by the use of ultraproducts they show that such extendability is (in certain precise sense) not an elementary property (Proposition 4). On the other hand they have some unexpected properties, especially in connexion with the relation 1/y0 + … + 1/yr = 1, and they have very small automorphism groups (Proposition 2 and Corollaries); and they are not unique factorization rings (Proposition 5), though they are integrally closed (Proposition 6).