Cancellation Property
In mathematics, the notion of cancellative is a generalization of the notion of invertible.
An element a in a magma (M,*) has the left cancellation property (or is left-cancellative) if for all b and c in M, a * b = a * c always implies b = c.
An element a in a magma (M,*) has the right cancellation property (or is right-cancellative) if for all b and c in M, b * a = c * a always implies b = c.
An element a in a magma (M,*) has the two-sided cancellation property (or is cancellative) if it is both left- and right-cancellative.
A magma (M,*) has the left cancellation property (or is left-cancellative) if all a in the magma are left cancellative, and similar definitions apply for the right cancellative or two-sided cancellative properties.
A left-invertible element is left-cancellative, and analogously for right and two-sided.
For example, every quasigroup, and thus every group, is cancellative.
Read more about Cancellation Property: Interpretation, Examples of Cancellative Monoids and Semigroups, Non-cancellative Algebras
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—Mark Twain [Samuel Langhorne Clemens] (1835–1910)