Let S be a totally ordered semigroup such that \(a0\) iff f(max s(f))\(>0\) becomes a totally ordered ring without zero divisors. It is well known that every totally ordered commutative field can be order embedded in some \({\mathbb{R}}((S))\). This paper presents a valuable contribution to the question which totally ordered rings without zero divisors are order embeddable in some \({\mathbb{R}}((S))\). An interesting consequence is the following: Every totally ordered division ring for which the group of archimedean classes is isomorphic to \(({\mathbb{Z}},+)\) is embeddable in the above sense.