In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation...
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In mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function...
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Inverse element (redirect from I-semigroup)
an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regular semigroups; these are I-semigroups in which...
30 KB (4,478 words) - 07:43, 4 July 2024
mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism...
25 KB (3,600 words) - 02:50, 16 March 2024
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...
28 KB (3,748 words) - 02:47, 3 May 2024
Markov operator (redirect from Markov semigroup)
linear or non-linear. Closely related to Markov operators is the Markov semigroup. The definition of Markov operators is not entirely consistent in the...
6 KB (1,078 words) - 15:40, 16 May 2024
Generating set of a group (redirect from Generator (semigroup))
{\displaystyle S} is a semigroup/monoid generating set of G {\displaystyle G} if G {\displaystyle G} is the smallest semigroup/monoid containing S {\displaystyle...
11 KB (1,746 words) - 14:56, 16 May 2023
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under...
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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...
1 KB (144 words) - 02:22, 13 May 2024
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...
9 KB (1,162 words) - 01:36, 20 December 2023
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...
12 KB (1,971 words) - 16:48, 14 May 2024
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...
35 KB (428 words) - 13:11, 9 April 2023
In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous. Every topological...
1 KB (224 words) - 05:46, 13 May 2024
In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the...
12 KB (1,445 words) - 08:27, 26 June 2024
Free monoid (redirect from Free Semigroup)
and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images...
22 KB (2,985 words) - 23:05, 23 February 2024
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...
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In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer...
2 KB (285 words) - 21:36, 10 August 2023
mathematics, an ordered semigroup is a semigroup (S,•) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x...
2 KB (213 words) - 10:05, 13 September 2020
Partial groupoid (section Partial semigroup)
partial groupoid ( G , ∘ ) {\displaystyle (G,\circ )} is called a partial semigroup if the following associative law holds: For all x , y , z ∈ G {\displaystyle...
2 KB (278 words) - 11:07, 26 December 2023
Monoid (category Semigroup theory)
with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of...
35 KB (4,447 words) - 08:24, 16 July 2024
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...
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Krohn–Rhodes theory (redirect from Finite semigroup)
result in finite semigroup theory, revealing a deep connection between finite automata and semigroups. Let T be a semigroup. A semigroup S that is a homomorphic...
19 KB (2,286 words) - 18:47, 16 August 2023
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating...
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definitions also apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the semigroup (multiplication) operation...
14 KB (2,097 words) - 17:21, 1 June 2024
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...
13 KB (1,417 words) - 07:17, 24 May 2024
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...
1 KB (170 words) - 02:12, 28 October 2022
Oscillator representation (redirect from Oscillator semigroup)
representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been...
106 KB (21,523 words) - 00:21, 25 May 2024
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic...
15 KB (496 words) - 06:51, 14 March 2023
a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having...
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Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with x x...
1 KB (113 words) - 11:43, 9 August 2017