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- Monoid abstract "In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are semigroups with identity. Monoids occur in several branches of mathematics; for instance, they can be regarded as categories with a single object. Thus, they capture the idea of function composition within a set. Monoids are also commonly used in computer science, both in its foundational aspects and in practical programming. The set of strings built from a given set of characters is a free monoid. The transition monoid and syntactic monoid are used in describing finite state machines, whereas trace monoids and history monoids provide a foundation for process calculi and concurrent computing. Some of the more important results in the study of monoids are the Krohn–Rhodes theorem and the star height problem. The history of monoids, as well as a discussion of additional general properties, are found in the article on semigroups.".
- Monoid wikiPageID "19652".
- Monoid wikiPageRevisionID "602923000".
- Monoid hasPhotoCollection Monoid.
- Monoid id "389".
- Monoid id "p/m064740".
- Monoid title "Monoid".
- Monoid urlname "Monoid".
- Monoid subject Category:Algebraic_structures.
- Monoid subject Category:Category_theory.
- Monoid subject Category:Semigroup_theory.
- Monoid type AlgebraicStructures.
- Monoid type Artifact100021939.
- Monoid type Object100002684.
- Monoid type PhysicalEntity100001930.
- Monoid type Structure104341686.
- Monoid type Whole100003553.
- Monoid type YagoGeoEntity.
- Monoid type YagoPermanentlyLocatedEntity.
- Monoid comment "In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are semigroups with identity. Monoids occur in several branches of mathematics; for instance, they can be regarded as categories with a single object. Thus, they capture the idea of function composition within a set.".
- Monoid label "Monoid".
- Monoid label "Monoid".
- Monoid label "Monoid".
- Monoid label "Monoide".
- Monoid label "Monoide".
- Monoid label "Monoide".
- Monoid label "Monoïde".
- Monoid label "Monoïde".
- Monoid label "Моноид".
- Monoid label "مونويد".
- Monoid label "モノイド".
- Monoid label "幺半群".
- Monoid sameAs Monoid.
- Monoid sameAs Monoid.
- Monoid sameAs Monoide.
- Monoid sameAs Monoïde.
- Monoid sameAs Monoide.
- Monoid sameAs モノイド.
- Monoid sameAs 모노이드.
- Monoid sameAs Monoïde.
- Monoid sameAs Monoid.
- Monoid sameAs Monoide.
- Monoid sameAs m.04z49.
- Monoid sameAs Q208237.
- Monoid sameAs Q208237.
- Monoid sameAs Monoid.
- Monoid wasDerivedFrom Monoid?oldid=602923000.
- Monoid isPrimaryTopicOf Monoid.