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...

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

Signed symmetric group and Generalized symmetric group Symmetry in quantum mechanics § Exchange symmetry Symmetric inverse semigroup Symmetric power Jacobson...

implies the existence of a unique inverse, but the opposite is not true. For example, in the symmetric inverse semigroup, the empty transformation Ø does...

: 81  Semiautomaton Krohn–Rhodes theory Symmetric inverse semigroup Biordered set Special classes of semigroups Composition ring Dominique Perrin; Jean...

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

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...

all partial bijections on a given base set is called the symmetric inverse semigroup. Another way of defining the same notion is to say that a partial...

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...

Representation theory of the symmetric group Schreier vector Strong generating set Symmetric group Symmetric inverse semigroup Weak order of permutations...

inverse may be defined on a *-regular semigroup. This abstract definition coincides with the one in linear algebra. Drazin inverse Hat matrix Inverse...

of a symmetric group (up to isomorphism). In the symmetric semigroup (of all transformations) one also finds a weaker, non-unique notion of inverse (called...

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

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

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

lemma Semigroup Subsemigroup Free semigroup Green's relations Inverse semigroup (or inversion semigroup, cf. [1]) Krohn–Rhodes theory Semigroup algebra...

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...

Laradji, A.; Umar, A. (2007), "Combinatorial results for the symmetric inverse semigroup", Semigroup Forum, 75 (1): 221–236, doi:10.1007/s00233-007-0732-8,...

equal to its converse is a symmetric relation; in the language of dagger categories, it is self-adjoint. Furthermore, the semigroup of endorelations on a set...

In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the...

with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of...

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 idempotent e in S. In the symmetric inverse...

an involution (on the real numbers) is symmetric across the line y = x. This is due to the fact that the inverse of any general function will be its reflection...

order of the symmetric group (See Lorscheid's article) – in the philosophy of the field with one element, one thus interprets the symmetric group as the...

S^{-1}:=\left\{s^{-1}:s\in S\right\}.} The closure of every symmetric set in a commutative topological group is symmetric. If S is any subset of a commutative topological...

of H. The same definitions apply more generally when G is an arbitrary semigroup, but this article will only deal with subgroups of groups. Suppose that...

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...

idempotents in a semigroup. The set of idempotents in a semigroup is a biordered set and every biordered set is the set of idempotents of some semigroup. A regular...

representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been...

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