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- Special_classes_of_semigroups abstract "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.In the algebraic theory of semigroups, in constructing special classes, attention is focused only on those properties, restrictions and conditions which can be expressed in terms of the binary operations in the semigroups and occasionally on the cardinality and similar properties of subsets of the underlying set. The underlying sets are not assumed to carry any other mathematical structures like order or topology.As in any algebraic theory, one of the main problems of the theory of semigroups is the classification of all semigroups and a complete description of their structure. In the case of semigroups, since the binary operation is required to satisfy only the associativity property the problem of classification is considered extremely difficult. Descriptions of structures have been obtained for certain special classes of semigroups. For example the structure of the sets of idempotents of regular semigroups is completely known. Structure descriptions are presented in terms of better known types of semigroups. The best known type of semigroup is the group.A (necessarily incomplete) list of various special classes of semigroups is presented below. To the extent possible the defining properties are formulated in terms of the binary operations in the semigroups. The references point to the locations from where the defining properties are sourced.".
- Special_classes_of_semigroups wikiPageExternalLink manual.pdf.
- Special_classes_of_semigroups wikiPageID "22653593".
- Special_classes_of_semigroups wikiPageLength "26244".
- Special_classes_of_semigroups wikiPageOutDegree "93".
- Special_classes_of_semigroups wikiPageRevisionID "655116001".
- Special_classes_of_semigroups wikiPageWikiLink Algebra.
- Special_classes_of_semigroups wikiPageWikiLink Algebraic_structure.
- Special_classes_of_semigroups wikiPageWikiLink American_Mathematical_Society.
- Special_classes_of_semigroups wikiPageWikiLink Aperiodic_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Archimedean_property.
- Special_classes_of_semigroups wikiPageWikiLink Associative.
- Special_classes_of_semigroups wikiPageWikiLink Associative_property.
- Special_classes_of_semigroups wikiPageWikiLink Band_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink Bicyclic_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Bijection.
- Special_classes_of_semigroups wikiPageWikiLink Binary_operation.
- Special_classes_of_semigroups wikiPageWikiLink Binary_relation.
- Special_classes_of_semigroups wikiPageWikiLink Brandt_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink CRC_Press.
- Special_classes_of_semigroups wikiPageWikiLink Cancellative_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Cardinality.
- Special_classes_of_semigroups wikiPageWikiLink Category:Algebraic_structures.
- Special_classes_of_semigroups wikiPageWikiLink Category:Semigroup_theory.
- Special_classes_of_semigroups wikiPageWikiLink Class_(set_theory).
- Special_classes_of_semigroups wikiPageWikiLink Classification_theorem.
- Special_classes_of_semigroups wikiPageWikiLink Classification_theorems.
- Special_classes_of_semigroups wikiPageWikiLink Clifford_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Commutative.
- Special_classes_of_semigroups wikiPageWikiLink Commutative_property.
- Special_classes_of_semigroups wikiPageWikiLink Completely_regular_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Composition_of_functions.
- Special_classes_of_semigroups wikiPageWikiLink Composition_of_relations.
- Special_classes_of_semigroups wikiPageWikiLink Cyclic_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink E-dense_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Empty_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Empty_set.
- Special_classes_of_semigroups wikiPageWikiLink Exponential.
- Special_classes_of_semigroups wikiPageWikiLink Field_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink Finite_set.
- Special_classes_of_semigroups wikiPageWikiLink Free_monoid.
- Special_classes_of_semigroups wikiPageWikiLink Free_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Full_transformation_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Function_composition.
- Special_classes_of_semigroups wikiPageWikiLink Group_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink India.
- Special_classes_of_semigroups wikiPageWikiLink Inverse_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink John_Wiley_&_Sons.
- Special_classes_of_semigroups wikiPageWikiLink Left_zero_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Linear_map.
- Special_classes_of_semigroups wikiPageWikiLink Linear_transformation.
- Special_classes_of_semigroups wikiPageWikiLink Map_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink Mathematics.
- Special_classes_of_semigroups wikiPageWikiLink Matrix_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink Monogenic_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Monoid.
- Special_classes_of_semigroups wikiPageWikiLink Nonempty_set.
- Special_classes_of_semigroups wikiPageWikiLink Nowhere_commutative_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Null_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Numerical_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Orthodox_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Oxford_University_Press.
- Special_classes_of_semigroups wikiPageWikiLink Partial_function.
- Special_classes_of_semigroups wikiPageWikiLink Partial_order.
- Special_classes_of_semigroups wikiPageWikiLink Partially_ordered_set.
- Special_classes_of_semigroups wikiPageWikiLink Property_(philosophy).
- Special_classes_of_semigroups wikiPageWikiLink Regular_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Right_zero_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Semiband.
- Special_classes_of_semigroups wikiPageWikiLink Semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Semigroup_with_involution.
- Special_classes_of_semigroups wikiPageWikiLink Semilattice.
- Special_classes_of_semigroups wikiPageWikiLink Set_(mathematics).
- Special_classes_of_semigroups wikiPageWikiLink Springer_Science+Business_Media.
- Special_classes_of_semigroups wikiPageWikiLink Structure.
- Special_classes_of_semigroups wikiPageWikiLink Subgroup.
- Special_classes_of_semigroups wikiPageWikiLink Subset.
- Special_classes_of_semigroups wikiPageWikiLink Symmetric_inverse_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Theory.
- Special_classes_of_semigroups wikiPageWikiLink Thiruvananthapuram.
- Special_classes_of_semigroups wikiPageWikiLink Topology.
- Special_classes_of_semigroups wikiPageWikiLink Transformation_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Trivial_semigroup.
- Special_classes_of_semigroups wikiPageWikiLink Underlying_set.
- Special_classes_of_semigroups wikiPageWikiLink University_of_Kerala.
- Special_classes_of_semigroups wikiPageWikiLink Vector_space.
- Special_classes_of_semigroups wikiPageWikiLink World_Scientific.
- Special_classes_of_semigroups wikiPageWikiLink Zero_semigroup.
- Special_classes_of_semigroups wikiPageWikiLinkText "Archimedean semigroups".
- Special_classes_of_semigroups wikiPageWikiLinkText "Special classes of semigroups".
- Special_classes_of_semigroups wikiPageWikiLinkText "Special classes of semigroups#List of special classes of semigroups".
- Special_classes_of_semigroups wikiPageWikiLinkText "orthodox semigroups".
- Special_classes_of_semigroups wikiPageWikiLinkText "special classes of semigroups".
- Special_classes_of_semigroups date "October 2012".
- Special_classes_of_semigroups hasPhotoCollection Special_classes_of_semigroups.
- Special_classes_of_semigroups reason "various, see talk".
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- Special_classes_of_semigroups wikiPageUsesTemplate Template:Cite_book.
- Special_classes_of_semigroups wikiPageUsesTemplate Template:Cleanup.
- Special_classes_of_semigroups wikiPageUsesTemplate Template:Doi.