In
mathematics, a
semigroup is a
nonempty set together with an
associative binary operation. A
special class of semigroups is a
class of
semigroups satisfying additional
properties or conditions. Thus the class of
commutative semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that
ab =
ba for all elements
a and
b in the semigroup. The class of
finite semigroups consists of those semigroups for which the
underlying set has finite
cardinality. Members of the class of Brandt semigroups are required to satisfy not just one condition but a set of additional properties. A large variety of special classes of semigroups have been defined though not all of them have been studied equally intensively.