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...

In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic...

{a} with operation a · a = a. Semigroup with two elements: there are five that are essentially different. A null semigroup on any nonempty set with a chosen...

semigroups with identity. Such algebraic structures occur in several branches of mathematics. The functions from a set into itself form a monoid with...

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...

i.e., if two elements of the semigroup have the same action, then they are equal. An analogue of Cayley's theorem shows that any semigroup can be realized...

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

interact with the semigroup operation. Two classes of U-semigroups have been studied: I-semigroups, in which the interaction axiom is aa°a = a *-semigroups, in...

that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations...

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...

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

define zero elements only in semigroups having at least two elements. In spite of its extreme triviality, the semigroup with one element is important in...

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 denoted...

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...

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...

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

apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the multiplication of the ring (a semigroup operation)...

S} is said to be a semigroup generating set of G {\displaystyle G} if each element of G {\displaystyle G} is a finite sum of elements of S {\displaystyle...

the sense used by Hausmann and Ore. Nevertheless, influential books in semigroup theory, including Clifford and Preston (1961) and Howie (1995) use groupoid...

In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number...

a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero...

{\displaystyle m\colon Q\to Q} . If s and t are two functions of the transformation semigroup, their semigroup product is defined as their function composition...

cancellative or two-sided cancellative properties. In a semigroup, a left-invertible element is left-cancellative, and analogously for right and two-sided. If...

commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements...

defined only for nonzero elements). In particular, the two definitions of a monomorphism are equivalent for sets, magmas, semigroups, monoids, groups, rings...

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)...

"canonical forms" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication...

In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses. The terminology was introduced by...

twentieth century. The fundamental notion involved is that of an arithmetic semigroup, which is a commutative monoid G satisfying the following properties:...

direct product of a right zero semigroup and a group, while a right abelian group is the direct product of a right zero semigroup and an abelian group. Left...