Algebra Solutions: Multiplication of residue classes of integers is associative

Prove that multiplication of residue classes in $\mathbb{Z}/(n)$ is associative. (You may assume that it is well defined.)

We have

$(\overline{a} \cdot \overline{b}) \cdot \overline{c}$	=	$\overline{a \cdot b} \cdot \overline{c}$
	=	$\overline{(a \cdot b) \cdot c}$
	=	$\overline{a \cdot (b \cdot c)}$
	=	$\overline{a} \cdot \overline{b \cdot c}$
	=	$\overline{a} \cdot (\overline{b} \cdot \overline{c})$ ,

since integer multiplication is associative.

Algebra Solutions