Integers under Multiplication form Semigroup

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Theorem

The set of integers under multiplication $\struct {\Z, \times}$ is a semigroup.


Proof

Closure

Integer Multiplication is Closed.

$\Box$


Associativity

Integer Multiplication is Associative.

$\Box$


The criteria for $\struct {\Z, \times}$ to be a semigroup are seen to be satisfied.

$\blacksquare$


Sources