Semigroups whose endomorphisms are power functions
Semigroups whose endomorphisms are power functions
For any commutative semigroup S and any positive integer m, the power function f:S→S defined by f(x)=x m is an endomorphism of S. In this paper we characterize finite cyclic semigroups as those finite commutative semigroups whose endomorphisms are power functions. We also prove that if S is a finite …