Category:Cancellability

From ProofWiki
Jump to navigation Jump to search

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.