Positive and negative parts in a lattice-ordered group
= Positive and negative parts in a lattice-ordered group
{title2=$g^+=g\vee1,\quad g^-=g^{-1}\vee1$}
The two positive parts satisfy $g=g^+(g^-)^{-1}$, commute with one another, and have <meet> one. They isolate positive and negative displacement in the pointwise model of a <lattice-ordered permutation group>. These are group elements, unlike the scalar positive part of a real number.