Piecewise syndetic set
In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. A set is called piecewise syndetic if there exists a finite subset G of such that for every finite sub
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
Cancellative semigroup
In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equa
Trace monoid
In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters t
Empty semigroup
In mathematics, a semigroup with no elements (the empty semigroup) is a semigroup in which the underlying set is the empty set. Many authors do not admit the existence of such a semigroup. For them a
Plactic monoid
In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified with semistandard Young tableaux. It was dis
Rational monoid
In mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a "normal form" that can be computed by a finite transducer: multiplication in such
Semigroup action
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 pro
Numerical semigroup
In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number and the binary operation is the operation of ad
Thick set
In mathematics, a thick set is a set of integers that contains arbitrarily long intervals. That is, given a thick set , for every , there is some such that .
Quantum Markov semigroup
In quantum mechanics, a quantum Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first introduced
IP set
In mathematics, an IP set is a set of natural numbers which contains all finite sums of some infinite set. The finite sums of a set D of natural numbers are all those numbers that can be obtained by a
3x + 1 semigroup
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating set of this semigroup are related to the seque
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. The number of distinct nonisomorphic semigroups with one eleme
Clifford semigroup
A Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup.It is an inverse semigroup with. Examples of Clifford semigroups are groups and comm
Special classes of semigroups
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
E-semigroup
In the area of mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup. Certain classes of E-semigroups have been studied long before the more
Free monoid
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid ope
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 = xyx and y = yxy, i.e
Refinement monoid
In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements c00, c01, c10, c11 of M such that a0=c00+c01, a1=
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
Bicyclic semigroup
In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. It is
Light's associativity test
In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The na
Weak inverse
In mathematics, the term weak inverse is used with several meanings.
Skew lattice
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 generalizat
Hille–Yosida theorem
In functional analysis, the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the speci
Quasicontraction semigroup
In mathematical analysis, a C0-semigroup Γ(t), t ≥ 0, is called a quasicontraction semigroup if there is a constant ω such that ||Γ(t)|| ≤ exp(ωt) for all t ≥ 0. Γ(t) is called a contraction semigroup
Transformation semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under function composition. If it includes the iden
Unavoidable pattern
In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet.
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. Since the same
Analytic semigroup
In mathematics, an analytic semigroup is particular kind of strongly continuous semigroup. Analytic semigroups are used in the solution of partial differential equations; compared to strongly continuo
Absorbing element
In mathematics, an absorbing element (or annihilating element) is a special type of element of a set with respect to a binary operation on that set. The result of combining an absorbing element with a
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 = x. The notion of weak inver
Krohn–Rhodes theory
In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of eleme
Lumer–Phillips theorem
In mathematics, the Lumer–Phillips theorem, named after Günter Lumer and Ralph Phillips, is a result in the theory of strongly continuous semigroups that gives a necessary and sufficient condition for
Completely regular semigroup
In mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regular semigroups forms an important subclass of the
Morphic word
In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automat
Semigroup with two elements
In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five distinct nonisomorphic semigroups having two elements:
* O2
Four-spiral semigroup
In mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen in a doctoral dissertation submitted to
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 = xn + 1. An aperiodic monoid is
Green's relations
In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named for James Alexand
Garside element
In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. Formally, if M is a monoid, then an element Δ of M is said to be a Gar
Splicing rule
In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language genera
Catholic semigroup
In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses. The terminology was introduced by B. M. Schein in a paper published in 1979. Every
Local language (formal language)
In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word
Recurrent word
In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquip
Semiautomaton
In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, a
Schutzenberger group
In abstract algebra, in semigroup theory, a Schutzenberger group is a certain group associated with a Green H-class of a semigroup. The Schutzenberger groups associated with different H-classes are di
Semigroup Forum
Semigroup Forum (print ISSN 0037-1912, electronic ISSN 1432-2137) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of
Invariant convex cone
In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms. The study of such cones was initiated by Ernest
History monoid
In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individ
Compact semigroup
In mathematics, a compact semigroup is a semigroup in which the sets of solutions to equations can be described by finite sets of equations. The term "compact" here does not refer to any topology on t
Brandt semigroup
In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also inverse semigroups. They are built in the sam
Principal factor
In algebra, the principal factor of a -class J of a semigroup S is equal to J if J is the kernel of S, and to otherwise.
C0-semigroup
In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar
Weight (strings)
The -weight of a string, for a letter , is the number of times that letter occurs in the string. More precisely, let be a finite set (called the alphabet), a letter of , and astring (where is the free
Presentation of a monoid
In algebra, a presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of relations on the free monoid Σ∗ (
Arf semigroup
In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by Cahit Arf. They appeared as the semigroups of values of Arf rings. A subset
Nilsemigroup
In mathematics, and more precisely in semigroup theory, a nilsemigroup or nilpotent semigroup is a semigroup whose every element is nilpotent.
Symmetric inverse semigroup
In abstract algebra, the set of all partial bijections on a set X (a.k.a. one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on
Monoid
In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid
Chinese monoid
In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a ≤ b ≤ c. An algorithm similar to Schensted's algorithm yields char
Biordered set
A biordered set (otherwise known as boset) is a mathematical object that occurs in the description of the structure of the set of idempotents in a semigroup. The set of idempotents in a semigroup is a
Monogenic semigroup
In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups.
Null semigroup
In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of a semigroup
Ordered semigroup
In mathematics, an ordered semigroup is a semigroup (S,•) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x ≤ y implies z•x ≤ z•y and x•z ≤ y•z for all x,
Syntactic monoid
In mathematics and computer science, the syntactic monoid of a formal language is the smallest monoid that recognizes the language .
Band (algebra)
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). Bands were first studied and named by A. H. Clif
Syndetic set
In mathematics, a syndetic set is a subset of the natural numbers, having the property of "bounded gaps": that the sizes of the gaps in the sequence of natural numbers is bounded.
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multip
Partial isometry
In functional analysis a partial isometry is a linear map between Hilbert spaces such that it is an isometry on the orthogonal complement of its kernel. The orthogonal complement of its kernel is call
Munn semigroup
In mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents). Munn semigroups are named for the Scotti
Zerosumfree monoid
In abstract algebra, an additive monoid is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally: This means that the only way zero can be expressed
Nowhere commutative semigroup
In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements of S are i
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. The basic example would be the three integers 0, 1, and −1,
Variety of finite semigroups
In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups having some nice algebraic properties. Those classes can be defined in two distinct ways
Regular semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that axa = a. Regular semigroups are one of th
Right group
In mathematics, a right group is an algebraic structure consisting of a set together with a binary operation that combines two elements into a third element while obeying the right group axioms. The r
Orthodox semigroup
In mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular E-semigroup. The term orthodo
Epigroup
In abstract algebra, an epigroup is a semigroup in which every element has a power that belongs to a subgroup. Formally, for all x in a semigroup S, there exists a positive integer n and a subgroup G
Sesquipower
In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix. Sesquipowers are unavoidable patterns, in the sense that all sufficiently long strings contai
Rees matrix semigroup
In mathematics, the Rees matrix semigroups are a special class of semigroups introduced by David Rees in 1940. They are of fundamental importance in semigroup theory because they are used to classify
Automatic semigroup
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines "cano