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semigroups

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Semigroups might refer to
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. * The binary operation of a semigroup is most often denoted multiplicatively: x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup. * The name "semigroup" originates in the fact that a semigroup generalizes a group by preserving only associativity and closure under the binary operation from the axioms defining a group while omitting the requirement for an identity element and inverses. From the opposite point of view (of adding rather than removing axioms), a semigroup is an associative magma. As in the case of groups or magmas, the semigroup operation need not be commutative, so x·y is not necessarily equal to y·x; a typical example of associative but non-commutative operation is matrix multiplication. If the semigroup operat

Semigroups might refer to

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
* The binary operation of a semigroup is most often denoted multiplicatively: x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup.
* The name "semigroup" originates in the fact that a semigroup generalizes a group by preserving only associativity and closure under the binary operation from the axioms defining a group while omitting the requirement for an identity element and inverses. From the opposite point of view (of adding rather than removing axioms), a semigroup is an associative magma. As in the case of groups or magmas, the semigroup operation need not be commutative, so x·y is not necessarily equal to y·x; a typical example of associative but non-commutative operation is matrix multiplication. If the semigroup operat

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