Title

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 ab if (a - b ) ≧ 0. Moreover, we let |a| = a v (- a).

Rights Information

© 1972 Institute of Mathematics AS CR