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.