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...

a semigroup is an associative magma. Empty semigroup: the empty set forms a semigroup with the empty function as the binary operation. Semigroup with...

In mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function...

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...

called the empty string and denoted by ε or λ, as the identity element. The free monoid on a set A is usually denoted A∗. The free semigroup on A is the...

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...

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...

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...

mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism...

mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...

nothing, a transformation semigroup can be made into a monoid by adding the identity function. Let M be a monoid and Q be a non-empty set. If there exists...

However, the integer 0 can not be expressed as a (non-empty) sum of 1s, thus {1} is not a semigroup generator of the natural numbers. Similarly, while {1}...

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...

inverse semigroups. They are built in the same way as completely 0-simple semigroups: Let G be a group and I , J {\displaystyle I,J} be non-empty sets....

mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen...

non-commutative non-band semigroups. Special classes of semigroups Semigroup with two elements Semigroup with one element Empty semigroup Andreas Distler, Classification...

they are used to classify certain classes of simple semigroups. Let S be a semigroup, I and Λ non-empty sets and P a matrix indexed by I and Λ with entries...

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...

with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of...

In mathematics, the Ellis–Numakura lemma states that if S is a non-empty semigroup with a topology such that S is a compact space and the product is semi-continuous...

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)...

In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups having some nice algebraic properties...

Triviality (mathematics) Examples of vector spaces Field with one element Empty semigroup Zero element List of zero terms David Sharpe (1987). Rings and factorization...

relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named...

element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is...

the second structure. For example: A semigroup homomorphism is a map between semigroups that preserves the semigroup operation. A monoid homomorphism is...

use this paper as the basis for a 1947 proof "that the word problem for semigroups was recursively insoluble", and later devised the canonical system for...

or occasionally as the full linear semigroup or general linear monoid. Notably, it constitutes a regular semigroup. If one removes the restriction of...

introduced this notion hoping to solve the word problem for finitely presented semigroups. Only in 1947 was the problem shown to be undecidable— this result was...

absorbing element in a multiplicative semigroup or semiring generalises the property 0 ⋅ x = 0. Examples include: The empty set, which is an absorbing element...