J Austral Math Soc Ser A 52 pp299--321, 1992.
(Received 1 October 1992; revised 21 December 1992)
A lattice-ordered power series algebra of a totally ordered field over a rooted abelian group may be constructed in a way that is arbitrary only in requiring that a factor set be chosen in the field and an extended total order be chosen on the group modulp its torsion subgroup. The resulting algebra is a field if and only if the subalgebra of elements with torsion support from a field. It follows that if the torsion subgroup may be independently embedded in the algebraic closure of the totally ordered field, or if the resulting algebra has no zero-divisors, then the algebra is a field. The set of supporting subsets for the power series may be characterized abstractly in such a way that previous representation theorems of lattice-ordered fields into power series algebras may be applied to produce representations into power series fields.
1991 AMS Subject Classification: primary 06F25; secondary 06F15, 12J15, 13J05, 16A27, 16A86
Last Modified: Mon Feb 3 9:46:11 2003