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

semigroup. The class of finite semigroups consists of those semigroups for which the underlying set has finite cardinality. Members of the class of Brandt...

are homomorphisms. The class of all semigroups forms a variety of algebras of signature (2), meaning that a semigroup has a single binary operation. A sufficient...

the class of null (left/right zero) semigroups is a variety of universal algebra, and thus a variety of finite semigroups. The variety of finite null semigroups...

nilsemigroups is not a variety of universal algebra. However, the set of finite nilsemigroups is a variety of finite semigroups. The variety of finite nilsemigroups...

generalization of the notion of finite words into a complete topological space. This notion allows the use of topology to study languages and finite semigroups. For...

spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well...

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"...

inverse semigroups are a subclass of *-semigroups. It is also textbook knowledge that an inverse semigroup can be characterized as a regular semigroup in which...

q-theory of Finite Semigroups. Springer Science & Business Media. p. 306. ISBN 978-0-387-09781-7. Eric Jespers; Jan Okniski (2007). Noetherian Semigroup Algebras...

all semigroups of order less than six are finitely based. In the theory of varieties of semigroups and universal algebras the problem of existence of covering...

and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal...

finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite...

notion generalizes to semigroups and, as such, is a central construction in the Krohn–Rhodes structure theory of finite semigroups. Let A {\displaystyle...

all completely 0-simple semigroups. All epigroups are also eventually regular semigroups. (also known as π-regular semigroups) A cancellative epigroup...

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

constraints on the algebraic structure, such as associativity (to form semigroups); identity, and inverses (to form groups); and other more complex structures...

group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the...

result of Askold Khovanskii on semigroups of lattice points. Later, Okounkov's construction was generalized and systematically developed in the papers of Robert...

representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of the general linear...

is that of an arithmetic semigroup, which is a commutative monoid G satisfying the following properties: There exists a countable subset (finite or countably...

product Types Simple group Finite group Abelian group Torsion subgroup Free abelian group Finitely generated abelian group Rank of an abelian group Cyclic...

geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The theory of fields proves that angle trisection and...

Convolution semigroups in L1 that form a nascent delta function are always an approximation to the identity in the above sense, however the semigroup condition...

ring. In particular, the center of a division ring is a field. It turned out that every finite domain (in particular finite division ring) is a field; in...

recognizable by a finite state automaton (related to the regular expression) Regular map (graph theory), a symmetric tessellation of a closed surface Regular...

four-group List of small groups Locally cyclic group Nilpotent group Non-abelian group Solvable group P-group Pro-finite group Classification of finite simple...

The number of fixed points of an involution on a finite set and its number of elements have the same parity. Thus the number of fixed points of all the involutions...

S\to T} from a finite commutative semigroup S to another semigroup T is surjective. Inverse semigroups are absolutely closed. Example of non-surjective...

alone imply that every element a of H generates a finite cyclic subgroup of H, say of order n, and then the inverse of a is an−1. If the group operation...