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36 relations: Additive number theory, Aperiodic semigroup, Automatic semigroup, Band (mathematics), Bicyclic semigroup, Brandt semigroup, Cancellative semigroup, Catholic semigroup, Commutative property, Commute, Completely regular semigroup, Cover (algebra), David Rees (mathematician), E-dense semigroup, Empty semigroup, Epigroup, Inverse element, Inverse semigroup, Matrix unit, Monogenic semigroup, Nambooripad order, Nowhere commutative semigroup, Numerical semigroup, Orthodox semigroup, Principal factor, Rees factor semigroup, Rees matrix semigroup, Regular semigroup, Semigroup, Semigroup with involution, Semigroup with three elements, Semigroup with two elements, Symmetric inverse semigroup, Transformation semigroup, Trivial semigroup, Variety of finite semigroups.
Additive number theory
In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition.
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Aperiodic semigroup
In mathematics, an aperiodic semigroup is a semigroup S such that every element x ∈ S is aperiodic, that is, for each x there exists a positive integer n such that xn.
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Automatic semigroup
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set.
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Band (mathematics)
In mathematics, a band (also called idempotent semigroup) is a semigroup in which every element is idempotent (in other words equal to its own square).
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Bicyclic semigroup
In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups.
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Brandt semigroup
In mathematics, Brandt semigroups are completely 0-simple inverse semigroups.
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Cancellative semigroup
In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property.
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Catholic semigroup
In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Commute
Commute, commutation or commutative may refer to.
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Completely regular semigroup
In mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup.
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Cover (algebra)
In abstract algebra, a cover is one instance of some mathematical structure mapping onto another instance, such as a group (trivially) covering a subgroup.
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David Rees (mathematician)
David Rees FRS (29 May 1918 – 16 August 2013) was a professor of pure mathematics at the University of Exeter, having been head of the Mathematics / Mathematical Sciences Department at Exeter for many years.
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E-dense semigroup
In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse x, meaning that xax.
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Empty semigroup
In mathematics, a semigroup with no elements (the empty semigroup) is a semigroup in which the underlying set is the empty set.
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Epigroup
In abstract algebra, an epigroup is a semigroup in which every element has a power that belongs to a subgroup.
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Inverse element
In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.
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Inverse semigroup
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x.
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Matrix unit
In mathematics, a matrix unit is an idealisation of the concept of a matrix, with a focus on the algebraic properties of matrix multiplication.
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Monogenic semigroup
In mathematics, a monogenic semigroup is a semigroup generated by a single element.
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Nambooripad order
In mathematics, Nambooripad order (also called Nambooripad's partial order) is a certain natural partial order on a regular semigroup discovered by K S S Nambooripad in late seventies.
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Nowhere commutative semigroup
In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab.
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Numerical semigroup
In mathematics, a numerical semigroup is a special kind of a semigroup.
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Orthodox semigroup
In mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup.
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Principal factor
In algebra, the principal factor of a \mathcal-class J of a semigroup S is equal to J if J is the kernel of S, and to J \cup \ otherwise.
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Rees factor semigroup
In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed using a semigroup and an ideal of the semigroup.
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Rees matrix semigroup
Rees matrix semigroups are a special class of semigroup introduced by David Rees in 1940.
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Regular semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a, there exists an element x such that axa.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semigroup with involution
In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application "cancelling itself out", and the same interaction law with the binary operation as in the case of the group inverse.
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Semigroup with three elements
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them.
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Semigroup with two elements
In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two.
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Symmetric inverse semigroup
In abstract algebra, the set of all partial bijections on a set X (one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is \mathcal_X or \mathcal_X In general \mathcal_X is not commutative.
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Transformation semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of functions from a set to itself that is closed under function composition.
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Trivial semigroup
In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one.
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Variety of finite semigroups
In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a set of semigroups having some nice algebraic properties.
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Redirects here:
0-simple, 0-simple semigroup, Commutative semigroup, Completely 0-simple semigroup, Completely 0-simple semigroups, Completely simple semigroup, Eventually regular semigroup, Pseudo-inverse semigroup, Pseudoinverse semigroup, Simple semigroup.
References
[1] https://en.wikipedia.org/wiki/Special_classes_of_semigroups
