Rings whose multiplicative endomorphisms are power functions (Q1955766)

If \(R\) is a commutative ring with identity, then for any positive integer \(m\) the power function \(f: R\rightarrow R\) defined by \(f(x)=x^m\) is an endomorphism of the multiplicative semigroup \((R,\cdot)\). The paper under review characterizes commutative rings \(R\) with identity, in which every multiplicative semigroup endomorphism is equal to a power function. It is proved that every multiplicative endomorphism \(f: R\rightarrow R\) is of the form \(f(x)=x^m\) for some positive integer \(m\), if and only if \(R\) is a finite field.