Definition:Multiplicative Monoid of Integers Modulo m
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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 $m$.
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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 $\eqclass 1 m$.