Definition:Modulo Multiplication/Definition 2
Jump to navigation
Jump to search
Definition
Let $m \in \Z$ be an integer.
Let $\Z_m$ be the set of integers modulo $m$:
- $\Z_m = \set {0, 1, \ldots, m - 1}$
The operation of multiplication modulo $m$ is defined on $\Z_m$ as:
Also denoted as
Although the operation of multiplication modulo $m$ is denoted by the symbol $\times_m$, if there is no danger of confusion, the conventional multiplication symbols $\times, \cdot$ etc. are often used instead.
The notation for multiplication of two integers modulo $m$ is not usually $\eqclass a m \times_m \eqclass b m$.
What is more normally seen is $a b \pmod m$.
Also see
- Results about modulo multiplication can be found here.
Sources
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Example $2.3$