Definition:Cancellable Element/Left Cancellable

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

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


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

Also see

 * Definition:Right Cancellable Element
 * Definition:Cancellable Element


 * Definition:Left Cancellable Operation


 * Definition:Cancellable Operation
 * Definition:Right Cancellable Operation