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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...

semigroups. There are also interesting classes of semigroups that do not contain any groups except the trivial group; examples of the latter kind are bands...

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

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...

non-equivalent semigroups, and OEIS: A023814 the number of associative binary operations, out of a total of nn2, determining a semigroup. Empty semigroup Trivial semigroup...

cardinality of S. The zero is the only idempotent of S. The trivial semigroup of a single element is trivially a nilsemigroup. The set of strictly upper triangular...

The second property implies that the empty product—that is, the trivial semigroup of one element—belongs to each variety. Hence a variety is necessarily...

contexts is group-free semigroup. In terms of Green's relations, a finite semigroup is aperiodic if and only if its H-relation is trivial. These two characterizations...

addition and the natural ordering. Every semigroup can be considered as a posemigroup endowed with the trivial (discrete) partial order "=". A morphism...

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...

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...

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...

groups and finite aperiodic semigroups of which S is a divisor. All finite aperiodic semigroups have complexity 0, while non-trivial finite groups have complexity...

element Empty semigroup Zero element List of zero terms David Sharpe (1987). Rings and factorization. Cambridge University Press. p. 10 : trivial ring. ISBN 0-521-33718-6...

In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the...

at least P.) In a semigroup S, the product of two subsets defines a structure of a semigroup on P(S), the power set of the semigroup S; furthermore P(S)...

{\displaystyle S} is a semigroup/monoid generating set of G {\displaystyle G} if G {\displaystyle G} is the smallest semigroup/monoid containing S {\displaystyle...

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)...

the structure admits no non-trivial congruence relations. The term is used differently in semigroup theory. A semigroup is said to be simple if it has...

the trivial (one-element) monoid, which is also the trivial group. Every group is a monoid and every abelian group a commutative monoid. Any semigroup S...