# Semigroup Theory: Monoid, Semigroup, Skew Lattice, Special Classes of Semigroups, Inverse Semigroup, Light's Associativity Test

## Source Wikipedia

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 47. Chapters: Monoid, Semigroup, Skew lattice, Special classes of semigroups, Inverse semigroup, Light's associativity test, Krohn-Rhodes theory, C0-semigroup, Green's relations, Biordered set, Semigroup with involution, Semigroup with two elements, Semigroup action, Trace monoid, Cancellative semigroup, Semiautomaton, Refinement monoid, Regular semigroup, Bicyclic semigroup, History monoid, Free monoid, Lumer-Phillips theorem, Band, Rees factor semigroup, Automatic semigroup, Hille-Yosida theorem, Presentation of a monoid, Transformation semigroup, Plactic monoid, Syntactic monoid, Schutzenberger group, Matrix unit, Analytic semigroup, IP set, Absorbing element, Partial isometry, Piecewise syndetic set, Monogenic semigroup, Null semigroup, Nowhere commutative semigroup, Garside element, Completely regular semigroup, Trivial semigroup, Empty semigroup, Aperiodic monoid, Weight, Levi's lemma, Chinese monoid, Weak inverse, Thick set, Strongly measurable functions, Arf semigroup, Quasicontraction semigroup, Ordered semigroup, Zerosumfree monoid. Excerpt: In abstract algebra, a skew lattice is an algebraic structure that is a non-commutative generalization of a lattice. While the term skew lattice can be used to refer to any non-commutative generalization of a lattice, over the past twenty years it has been used primarily as follows. A skew lattice is a set S equipped with two associative, idempotent binary operations and , called meet and join, that satisfy the following dual pair of absorption laws and .Given that and are associative and idempotent, these identities are equivalent to the dualities: iff and iff . For over 60 years, noncommutative variations of lattices have been studied with differing motivations. For some the motivation has been an interest in the conceptual boundaries of lattice theory; for others it was a search ...

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