= Cover of a value in a lattice-ordered group
{title2=$V^*=\langle V,t\rangle_c$}
If $V$ is a <value in a lattice-ordered group> of $t>1$, every <convex lattice subgroup> strictly containing $V$ contains $t$. Thus the convex lattice subgroup generated by $V$ and $t$ is the unique least subgroup properly containing $V$. It is called the cover of $V$. There is no intermediate <convex lattice subgroup>. A <normal-valued lattice-ordered group> requires $V$ to be a <normal subgroup> of this cover, not necessarily of the whole group. Values are <prime convex lattice subgroups>: maximality omitting $t$ makes them meet-irreducible in the <lattice of convex lattice subgroups>, so their ordered right cosets form a chain.
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