Integrally closed and complete ordered quasigroups and loops
Integrally closed and complete ordered quasigroups and loops
We generalize the well-known results on embedding a partially ordered group in its Dedekind extension by showing that, with the appropriate definition of <italic>integral closure</italic>, any partially ordered quasigroup (loop) <italic>G</italic> can be embedded in a complete partially ordered quasigroup (loop) if and only if <italic>G</italic> is integrally closed. If …