Definition:Multiplicative Monoid of Integers Modulo m

Definition
Let $m \in \Z$ such that $m > 1$.

The multiplicative monoid of integers modulo $m$ $\struct {\Z_m, \times_m}$ is the set of integers modulo $m$ under the operation of multiplication modulo $m$.

Also see

 * Definition:Multiplicative Group of Reduced Residues


 * Integers Modulo m under Multiplication form Commutative Monoid

Thus multiplication modulo $m$ is:


 * Well-defined on $\Z_m$
 * Closed on $\Z_m$
 * Associative on $\Z_m$
 * Commutative on $\Z_m$
 * The identity of $\struct {\Z_m, \times_m}$ is $\eqclass 1 m$.