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- Semigroup abstract "In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that a semigroup need not have an identity element. It also (originally) generalized a group (a monoid with all inverses) in that no element had to have an inverse, thus the name semigroup.The binary operation of a semigroup is most often denoted multiplicatively: , or simply , denotes the result of applying the semigroup operation to the ordered pair . The operation is required to be associative so that for all x, y and z, but need not be commutative so that does not have to equal (contrast to the standard multiplication operator on real numbers, where xy = yx).By definition, a semigroup is an associative magma. A semigroup with an identity element is called a monoid. A group is then a monoid in which every element has an inverse element. Semigroups must not be confused with quasigroups which are sets with a not necessarily associative binary operation such that division is always possible.The formal study of semigroups began in the early 20th century. Semigroups are important in many areas of mathematics because they are the abstract algebraic underpinning of "memoryless" systems: time-dependent systems that start from scratch at each iteration. In applied mathematics, semigroups are fundamental models for linear time-invariant systems. In partial differential equations, a semigroup is associated to any equation whose spatial evolution is independent of time. The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata. In probability theory, semigroups are associated with Markov processes (Feller 1971).".
- Semigroup wikiPageID "27799".
- Semigroup wikiPageRevisionID "598655380".
- Semigroup hasPhotoCollection Semigroup.
- Semigroup subject Category:Algebraic_structures.
- Semigroup subject Category:Semigroup_theory.
- Semigroup type AlgebraicStructures.
- Semigroup type Artifact100021939.
- Semigroup type Object100002684.
- Semigroup type PhysicalEntity100001930.
- Semigroup type Structure104341686.
- Semigroup type Whole100003553.
- Semigroup type YagoGeoEntity.
- Semigroup type YagoPermanentlyLocatedEntity.
- Semigroup comment "In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that a semigroup need not have an identity element.".
- Semigroup label "Demi-groupe".
- Semigroup label "Halbgruppe".
- Semigroup label "Halfgroep".
- Semigroup label "Półgrupa".
- Semigroup label "Semigroup".
- Semigroup label "Semigrupo".
- Semigroup label "Semigrupo".
- Semigroup label "Semigruppo".
- Semigroup label "Полугруппа".
- Semigroup label "نصف زمرة".
- Semigroup label "半群".
- Semigroup label "半群".
- Semigroup sameAs Pologrupa.
- Semigroup sameAs Halbgruppe.
- Semigroup sameAs Semigrupo.
- Semigroup sameAs Demi-groupe.
- Semigroup sameAs Semigruppo.
- Semigroup sameAs 半群.
- Semigroup sameAs 반군.
- Semigroup sameAs Halfgroep.
- Semigroup sameAs Półgrupa.
- Semigroup sameAs Semigrupo.
- Semigroup sameAs m.06xtc.
- Semigroup sameAs Q207348.
- Semigroup sameAs Q207348.
- Semigroup sameAs Semigroup.
- Semigroup wasDerivedFrom Semigroup?oldid=598655380.
- Semigroup isPrimaryTopicOf Semigroup.