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- Semigroup_action abstract "In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations. The terminology conveys the idea that the elements of the semigroup are acting as transformations of the set. From an algebraic perspective, a semigroup action is a generalization of the notion of a group action in group theory. From the computer science point of view, semigroup actions are closely related to automata: the set models the state of the automaton and the action models transformations of that state in response to inputs.An important special case is a monoid action or act, in which the semigroup is a monoid and the identity element of the monoid acts as the identity transformation of a set. From a category theoretic point of view, a monoid is a category with one object, and an act is a functor from that category to the category of sets. This immediately provides a generalization to monoid acts on objects in categories other than the category of sets.Another important special case is a transformation semigroup. This is a semigroup of transformations of a set, and hence it has a tautological action of on that set. This concept is linked to the more general notion of a semigroup by an analogue of Cayley's theorem.(A note on terminology: the terminology used in this area varies, sometimes significantly, from one author to another. See the article for details.)".
- Semigroup_action wikiPageID "1058218".
- Semigroup_action wikiPageLength "11280".
- Semigroup_action wikiPageOutDegree "41".
- Semigroup_action wikiPageRevisionID "674902753".
- Semigroup_action wikiPageWikiLink Algebra.
- Semigroup_action wikiPageWikiLink Algebraic_structure.
- Semigroup_action wikiPageWikiLink Associative_property.
- Semigroup_action wikiPageWikiLink Automata_theory.
- Semigroup_action wikiPageWikiLink Binary_operation.
- Semigroup_action wikiPageWikiLink Category:Semigroup_theory.
- Semigroup_action wikiPageWikiLink Category:Theoretical_computer_science.
- Semigroup_action wikiPageWikiLink Category_(mathematics).
- Semigroup_action wikiPageWikiLink Category_of_sets.
- Semigroup_action wikiPageWikiLink Category_theory.
- Semigroup_action wikiPageWikiLink Cayleys_theorem.
- Semigroup_action wikiPageWikiLink Currying.
- Semigroup_action wikiPageWikiLink Deterministic_finite_automaton.
- Semigroup_action wikiPageWikiLink Finite-state_machine.
- Semigroup_action wikiPageWikiLink Free_monoid.
- Semigroup_action wikiPageWikiLink Function_composition.
- Semigroup_action wikiPageWikiLink Geometric_transformation.
- Semigroup_action wikiPageWikiLink Group_(mathematics).
- Semigroup_action wikiPageWikiLink Group_action.
- Semigroup_action wikiPageWikiLink Identity_element.
- Semigroup_action wikiPageWikiLink Identity_function.
- Semigroup_action wikiPageWikiLink Image_(mathematics).
- Semigroup_action wikiPageWikiLink Injective_function.
- Semigroup_action wikiPageWikiLink Isomorphism.
- Semigroup_action wikiPageWikiLink Module_(mathematics).
- Semigroup_action wikiPageWikiLink Monoid.
- Semigroup_action wikiPageWikiLink Ring_(mathematics).
- Semigroup_action wikiPageWikiLink Semiautomaton.
- Semigroup_action wikiPageWikiLink Semigroup.
- Semigroup_action wikiPageWikiLink Set_(mathematics).
- Semigroup_action wikiPageWikiLink String_(computer_science).
- Semigroup_action wikiPageWikiLink Theoretical_computer_science.
- Semigroup_action wikiPageWikiLink Transformation_semigroup.
- Semigroup_action wikiPageWikiLinkText "Compatibility".
- Semigroup_action wikiPageWikiLinkText "S-acts".
- Semigroup_action wikiPageWikiLinkText "Semigroup action".
- Semigroup_action wikiPageWikiLinkText "a correspondence between the two notions".
- Semigroup_action wikiPageWikiLinkText "acting faithfully".
- Semigroup_action wikiPageWikiLinkText "action".
- Semigroup_action wikiPageWikiLinkText "compatible".
- Semigroup_action wikiPageWikiLinkText "semigroup action".
- Semigroup_action wikiPageUsesTemplate Template:Main.
- Semigroup_action wikiPageUsesTemplate Template:Reflist.
- Semigroup_action subject Category:Semigroup_theory.
- Semigroup_action subject Category:Theoretical_computer_science.
- Semigroup_action hypernym Rule.
- Semigroup_action type Area.
- Semigroup_action type Country.
- Semigroup_action type Area.
- Semigroup_action comment "In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations. The terminology conveys the idea that the elements of the semigroup are acting as transformations of the set.".
- Semigroup_action label "Semigroup action".
- Semigroup_action sameAs Q7449424.
- Semigroup_action sameAs Ação_de_semigrupo.
- Semigroup_action sameAs m.042bnj.
- Semigroup_action sameAs Q7449424.
- Semigroup_action wasDerivedFrom Semigroup_action?oldid=674902753.
- Semigroup_action isPrimaryTopicOf Semigroup_action.