Computing the inversion height of some embeddings of the free algebra and the free group algebra

Let X be a set and k a field. We show the so-called JF-embeddings of k(X) in a division ring have inversion height at most two, and give examples of inversion height one and two. We use these embeddings to obtain embeddings of the free group algebra in a division ring of inversion height one and two. (c) 2006 Elsevier Inc. All rights reserved.