Monoid automorphism
= Monoid automorphism
A monoid automorphism is a bijective operation- and identity-preserving self-map of a <monoid>. Its inverse is also a monoid homomorphism. Permuting <prime numbers> and extending by <prime factorization> gives all automorphisms of the multiplicative monoid of positive natural numbers; extending by $0\mapsto0$ gives automorphisms of the multiplicative monoid including zero.