On orderings, valuations and 0-primes of a commutative ring (Q919041)

This paper examines the interplay between the orderings and valuations of a commutative ring R. When R is a field, this is a well-known area of study. Topics studied in this paper include: conditions for R to be semi- real (-1 is not a sum of squares in R) in terms of the 0-primes of R, compatibility of valuations and orderings of R, and various topologies on certain sets of valuations of R when R is semi-real. Several examples are given to illustrate the theory.