RATIONAL CLOSURES OF GROUP RINGS OF LEFT-ORDERED GROUPS

Suppose is a division ring, and is a left-ordered group such that for any Dedekind cut of the linearly ordered set the group is such that is a right Ore domain and the group is cofinal in . Then the group ring can be embedded in a division ring having a valuation in the sense of Mathiak with values in . If is the group of a trifolium, this construction leads to an example of a chain domain with a prime, but not completely prime, ideal.Bibliography: 9 titles.