The convex lattice subgroups of a lattice-ordered group form a distributive lattice, with intersection as meet and the convex lattice subgroup generated by a union as join. A positive element of a join is bounded by a finite product of positive elements from the generating subgroups. Riesz decomposition in a lattice-ordered group splits such an element into positive factors from those subgroups. If the original element belongs to another convex subgroup , every factor does too. Consequently .

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  1. Convex lattice subgroup
  2. Lattice-ordered group
  3. Partially ordered group
  4. Group
  5. Group theory
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