nLab
cancellative monoid

Contents

Definition

A commutative monoid (A,)(A, \cdot) is called cancellative if

a,b,zA((az=bz)(a=b)) \underset{a,b,z \in A}{\forall} \left( \left( a \cdot z = b \cdot z \right) \Rightarrow \left( a = b \right) \right)

For a non-commutative monoid one distinguishes left and right cancellability, in the evident way

References

See also

Last revised on May 30, 2017 at 10:20:46. See the history of this page for a list of all contributions to it.