On Difficulties in Embedding Lattice-Ordered Integral Domains In Lattice-Ordered Fields
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).
© 1972 Institute of Mathematics AS CR
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. .