Semigroups satisfying \(xy=yg(x,y)x\)
Tamura proved that if every group that satisfies an identity of the form \(xy=yg(x,y)x\) is commutative, then so is every semigroup that satisfies that identity. The result was obtained as a consequence of a general structure theorem for semigroups that satisfy the identity. This note presents a short proof that bypasses the structure theorem.
scientific article; zbMATH DE number 4004481