Embedding simple commutative monoids into simple refinement monoids

Details Embedding simple commutative monoids into simple refinement monoids Embedding simple commutative monoids into simple refinement monoids

2005-03-08

arxiv.org/abs/math/0503155v1

Semigroup Forum 56 (1998) 104--129

Mathematics

General Mathematics

Scientific paper

Say that a cone is a commutative monoid in which x+y=0 implies that x=y=0. We show that cones (resp. simple cones) of many kinds order-embed or even embed unitarily into refinement cones (resp. simple refinement cones) of the same kind, satisfying in addition various divisibility conditions. We do this in particular for all cones, or for all separative cones, or for all cancellative cones (positive cones of partially ordered abelian groups). We also settle both the torsion-free case and the unperforated case. Most of our results extend to arbitrary commutative monoids.

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