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We generalize the well-known results on embedding a partially ordered group in its Dedekind extension by showing that, with the appropriate definition of integral closure, anv partiallv ordered quasigroup (loop) G can be embedded in a complete partially ordered quasigroup (loop) if and only if G is integrally closed. If G is directed as well, then its Dedekind extension is a complete lattice-ordered quasigroup (loop). Furthermore, any complete fully ordered quasigroup (loop) has, with onedoi:10.1090/s0002-9939-1972-0295985-3 fatcat:qilybjlz4zf67hb5a6gjpvhbiq