- 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...
-
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...
-
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...
- 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...
- D and J
coincide for any epigroup. If S is an epigroup, any
regular subsemigroup of S is also an epigroup. In an
epigroup the
Nambooripad order (as extended...
- 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...
-
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...
