## Related questions with answers

Question

Construct the affine plane AP(Z3). Determine its parallel classes and the corresponding Latin squares for the classes of finite nonzero slope.

Solution

VerifiedStep 1

1 of 4The set of points of the plane $\textup{AP}(\mathbb{Z}_3)$ is

$\left\lbrace (x,y) : x,y \in \mathbb{Z}_3 \right\rbrace$

The lines are $x = a$, $a \in \mathbb{Z}_3$ and $y = ax+b$, $a,b \in \mathbb{Z}_3$.

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