symmetric inverse semigroup
Let be a set. A partial map on is an application defined from a subset of into . We denote by the set of partial map on . Given , we denote by and respectively the domain and the range of , i.e.
We define the composition of two partial map as the partial map with domain
defined by the common rule
It is easily verified that the with the composition is a semigroup.
A partial map is said bijective when it is bijective as a map . It can be proved that the subset of the partial bijective maps on is an inverse semigroup (with the composition ), that is called symmetric inverse semigroup on . Note that the symmetric group on is a subgroup of .
|Title||symmetric inverse semigroup|
|Date of creation||2013-03-22 16:11:14|
|Last modified on||2013-03-22 16:11:14|
|Last modified by||Mazzu (14365)|
|Defines||composition of partial maps|
|Defines||symmetric inverse semigroup|