Abstract algebra MOC

Quasigroup

A quasigroup is a group-like structure that need not be associative. Formally, a quasigroup is a magma such that for any there exist unique such that algebra

called the Latin square property since it requires that the resulting Cayley table form a Latin square. Equivalently, we may characterize a quasigroup as having left and right division satisfying the following identities (i.e. for all )

Proof of equivalence

proof

---

develop | en | sembr