theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in...

inverse. If every element has exactly one inverse as defined in this section, then the semigroup is called an inverse semigroup. Finally, an inverse semigroup...

we mention: regular semigroups, orthodox semigroups, semigroups with involution, inverse semigroups and cancellative semigroups. There are also interesting...

an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on...

group inverse. It is thus not a surprise that any group is a semigroup with involution. However, there are significant natural examples of semigroups with...

the notion of regularity be applied to semigroups was first made by David Rees. The term inversive semigroup (French: demi-groupe inversif) was historically...

the bicyclic semigroup is an inverse semigroup. (This means that each element x of B has a unique inverse y, in the "weak" semigroup sense that x y...

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

X^{-1}})^{+}} we obtain a presentation (for an inverse semigroup) ( X ; T ) {\displaystyle (X;T)} and an inverse semigroup I n v ⟨ X | T ⟩ {\displaystyle \mathrm...

mathematics, the term weak inverse is used with several meanings. In the theory of semigroups, a weak inverse of an element x in a semigroup (S, •) is an element...

In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under...

forms an important subclass of the class of regular semigroups, the class of inverse semigroups being another such subclass. Alfred H. Clifford was the...

e = ef = fe. Vagner in 1952 had extended this to inverse semigroups as follows: For any a and b in an inverse semigroup S, a ≤ b if and only if a = eb for some...

matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes...

mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents)...

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...

inverse may refer to: the inverse element in a group or in a subgroup of another, not necessarily group structure, e.g. in a subgroup of a semigroup the...

symmetric semigroup (of all transformations) one also finds a weaker, non-unique notion of inverse (called a pseudoinverse) because the symmetric semigroup is...

Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with x x...

shown for inverse semigroups: every inverse semigroup admits an F-inverse cover. McAlister's covering theorem generalizes to orthodox semigroups: every orthodox...

a regular semigroup that is also an E-semigroup is known as an orthodox semigroup. Weipoltshammer proved that the notion of weak inverse (the existence...

slightly modified when one deals with semigroups or monoids. Indeed, this definition should not use the notion of inverse operation anymore. The set S {\displaystyle...

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...

all partial bijections on X {\displaystyle X} forms the symmetric inverse semigroup. Charts in the atlases which specify the structure of manifolds and...

semigroup under this operation, the subsemigroup of idempotents being { a, b, c }. Inverse semigroups and bands are examples of orthodox semigroups....

elements of S are inverses of each other. Nowhere commutative semigroups can be characterized in several different ways. If S is a semigroup then the following...

algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse x, meaning that...

multiplicative inverse Semigroup – an algebraic structure consisting of a set together with an associative binary operation Monoid – a semigroup with an identity...

transformation Unitary representation Unitarity (physics) E-unitary inverse semigroup Unitary authority Unitary state Unital (disambiguation) Unitarianism...

= |x|). Monoid Inverse function Involution (mathematics) Multiplicative inverse Reflection (mathematics) Reflection symmetry Semigroup Gallian, Joseph...