left identity and right identity
An element which is both a left and a right identity is an identity element.
A groupoid may have more than one left identify element: in fact the operation defined by for all defines a groupoid (in fact, a semigroup) on any set , and every element is a left identity.
But as soon as a groupoid has both a left and a right identity, they are necessarily unique and equal. For if is a left identity and is a right identity, then .
|Title||left identity and right identity|
|Date of creation||2013-03-22 13:02:05|
|Last modified on||2013-03-22 13:02:05|
|Last modified by||mclase (549)|