The quotient fields of a class of lattice-ordered commutative domains
by
Jingjing Ma
The University of Texas at El Paso

Let R be a lattice-ordered ring and a commutative domain. Based on Steinberg's work on the quotient rings of lattice-ordered rings, it is shown that if R is algebraic over a subring which is totally ordered and whose positive elements are d-elements of R (an element r of R is called a d-element of R if the multiplication by r is an l-endormorphism of the underlying lattice-ordered group of R), then the quotient field of R can be made into a lattice-ordered ring extension of R. Moreover, if R is Archimedean, then, by directly using Schwartz's results on Archimedean lattice-ordered fields, the lattice order is extendible to a total order on R. Finally we consider some properties of d-elements.

Date received: February 13, 2000