Commutativity theorems for cancellative semigroups (Q1702517)

The authors show that a cancellative semigroup admitting commutators and satisfying a functional equation \([f(x),y]=[x,g(y)f(y)]\) implies that the element \(g(y)\) is central. They also use the result to show that a cancellative semigroup admitting commutators and satisfying the identity \([x^n ,y]=[x,y^{n+k}]\) implies that the element \(y^k\) is central. Taking \(k=1\) in the previous result yields the commutativity theorem by \textit{E. Psomopoulos} [Int. J. Math. Math. Sci. 7, 513--517 (1984; Zbl 0561.16013)] in group theory.