Old results about f-rings, revisited
by
Stuart Steinberg
University of Toledo

The Henriksen-Isbell description of unitable f-rings holds in a more general setting. If C is a commutative directed po-ring with a positive identity and R is an f-algebra over C, we investigate when R is C-unitable, that is, when can R be embedded in a unital C-f-algebra. Not every torsion-free unitable f-algebra over a totally ordered domain is C-unitable. We determine those semiprime f-rings C over which unitability implies C-unitability. For these base rings and also in the torsion-free case C-unital covers are unique, but they are not unique, in general.

Date received: February 16, 2000