# On Difficulties in Embedding Lattice-Ordered Integral Domains In Lattice-Ordered Fields

## Document Type

Article

## Department

Mathematics (HMC)

## Publication Date

1972

## Abstract

A *lattice ordered ring* (or *l-ring*) *A = A*(*+, *•, v, ʌ) is an abstract algebra closed under four binary operations *+, *•, v, ʌ such that *A*(*+, *•) is a ring, *A*(v, ʌ) is a lattice, and if 0 is the identity element of *A*(+), then

*a, b *≧ 0 imply that *a *+ *b* ≧ 0 and a • b ≧ 0.

As usual, we say that *a* ≧ 0 if *a* v 0 = *a*, and *a* ≧ *b* if (*a* - *b* ) ≧ 0. Moreover, we let |*a*| = *a* v (- *a*).

## Rights Information

© 1972 Institute of Mathematics AS CR

## Recommended Citation

Henriksen, M.. "On difficulties in embedding lattice-ordered integral domains in lattice-ordered fields." General Topology and its Relations to Modern Analysis and Algebra. Praha: Academia Publishing House of the Czechoslovak Academy of Sciences, 1972. 183-185. .