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This category contains results about cancellable elements.

Let $\left ({S, \circ}\right)$ be an algebraic structure.

An element $x \in \left ({S, \circ}\right)$ is cancellable if and only if:

$\forall a, b \in S: x \circ a = x \circ b \implies a = b$
$\forall a, b \in S: a \circ x = b \circ x \implies a = b$

... that is, it is both left cancellable and right cancellable.