Enunciato


$(\Z/_\equiv, +, \cdot )$ è un Anello commutativo unitario. (Anello delle classi resto modulo $m$)

Esempio


$m= 3 \Longrightarrow \Z/_\equiv = \{[r] : 0 \leq r \leq 2 \}=\{[0],[1],[2]\}$

Tabella Additiva $(+)$

$$ \begin{array}{c|ccc} & [0] & [1] & [2] \\ \hline [0] & [0] & [1] & [2] \\ [1] & [1] & [2] & [0] \\ [2] & [2] & [0] & [1] \end{array} $$

$$ [1]+[2] = [1+2] = [3] = [0] \\ [2]+[2] = [2+2] = [4] = [1] $$

Tabella Moltiplicativa $(\cdot)$

$$ \begin{array}{c|ccc} & [0] & [1] & [2] \\ \hline [0] & [0] & [0] & [0] \\ [1] & [0] & [1] & [2] \\ [2] & [0] & [2] & [1] \end{array} $$

$$ [2][2]=[2\cdot2]=[4]=[1] $$