Definition of Subsemigroup. Meaning of Subsemigroup. Synonyms of Subsemigroup

- then the intersection of any collection of subsemigroups of S is also a subsemigroup of S. So the subsemigroups of S form a complete lattice. An example...
- similarly named notion for a semigroup is defined likewise and it is a subsemigroup. The center of a ring (or an ****ociative algebra) R is the subset of...
- two elements as subsemigroups. In the example above, the set {−1,0,1} under multiplication contains both {0,1} and {−1,1} as subsemigroups (the latter is...
- clearly do) will obey the cancellative law. In a different vein, (a subsemigroup of) the multiplicative semigroup of elements of a ring that are not zero...
- Let T be a semigroup. A semigroup S that is a homomorphic image of a subsemigroup of T is said to be a divisor of T. The Krohn–Rhodes theorem for finite...
- sx=xs{\text{ for every }}s\in S\}.} Then S ′ {\displaystyle S'} forms a subsemigroup and S ′ = S ‴ = S ′′′′′ {\displaystyle S'=S'''=S'''''} ; i.e. a commutant...
- monoid on a set A is usually denoted A∗. The free semigroup on A is the subsemigroup of A∗ containing all elements except the empty string. It is usually...
- theory, a maximal subgroup of a semigroup S is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation) of S which is not...
- actually hold for any element a of an arbitrary semigroup and the monogenic subsemigroup ⟨ a ⟩ {\displaystyle \langle a\rangle } it generates. A related notion...
- 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...