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

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

(xy)−1 = (y)−1(x)−1. Taken as an axiom, it leads to the notion of semigroup with involution, of which there are natural examples that are not groups, for...

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...

numbers with complex conjugation, the real numbers are the Hermitian elements, and the imaginary numbers are the skew Hermitian. Semigroup with involution B*-algebra...

an involution, and typically denoted by a* Clearly a group is both an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory...

composition of an antihomomorphism with a homomorphism gives another antihomomorphism. Semigroup with involution Jacobson, Nathan (1943). The Theory...

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

} which is taken as an axiom in the more general context of a semigroup with involution, has sometimes been called an antidistributive property (of inversion...

relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more...

operation on B ( X ) {\displaystyle {\mathcal {B}}(X)} , it forms a semigroup with involution. Some important properties that a homogeneous relation R {\displaystyle...

presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of...

This property makes the set of all binary relations on a set a semigroup with involution. The composition of (partial) functions (that is, functional relations)...

can be defined in the more abstract setting of a semigroup with involution; the definition coincides with the one herein. In finite-dimensional vector spaces...

single binary operation over S. Semigroup: an associative magma. Monoid: a semigroup with identity element. Group: a monoid with a unary operation (inverse)...

Monoid Inverse function Involution (mathematics) Multiplicative inverse Reflection (mathematics) Reflection symmetry Semigroup Gallian, Joseph A. (2017)...

Chinese monoid equivalence class of a permutation is the preimage of an involution under the map w ↦ w ∘ w − 1 {\displaystyle w\mapsto w\circ w^{-1}} where...

complemented lattice. An orthocomplementation on a complemented lattice is an involution that is order-reversing and maps each element to a complement. An orthocomplemented...

has been generalized to form algebras of dimension 2n over a field F with involution. The square function z2 is the "norm" of the composition algebra C...

sometimes referred to as complete residuated semigroups. A quantale is a complete lattice Q {\displaystyle Q} with an associative binary operation ∗ : Q ×...

N(xy)=N(x)N(y)} for all x and y in A. A composition algebra includes an involution called a conjugation: x ↦ x ∗ . {\displaystyle x\mapsto x^{*}.} The quadratic...

algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation...

Theorem: A semiheap with a biunitary element e may be considered an involuted semigroup with operation given by ab = [a, e, b] and involution by a–1 = [e, a...

operators on a Hilbert space are a Baer ring and is also a Baer *-ring with the involution * given by the adjoint. von Neumann algebras are examples of all...

ISBN 3-540-63246-8 Novák, Vítězslav (1996), "Ternary structures and partial semigroups", Czechoslovak Mathematical Journal, 46 (1): 111–120, hdl:10338.dmlcz/127275...

is the convex polytope with vertices w(X) where w runs over the Weyl group. Let G be a compact Lie group and σ an involution with K a compact subgroup fixed...

1980. (with F. Pastijn) "V-regular semigroup". Proceedings of Royal Society of Edinburgh 88A : 275–291. 1981. (with F. Pastjin) "Regular involution semigroups"...

that map to the identity under the natural map from the free monoid with involution on A {\displaystyle A} to the group G {\displaystyle G} . If B {\displaystyle...

Consider the field of complex numbers equipped with the identity involution (as opposed to the involution considered elsewhere in the article); do there...

underlying Banach space, which turns them into Banach algebras. If an involution is given as well, we obtain B*-algebras and C*-algebras. These are studied...