Concept in mathematics regarding sets operating on groups
In abstract algebra, a branch of mathematics, a group with operators or Ω-group is an algebraic structure that can be viewed as a group together with a set Ω that operates on the elements of the group in a special way.
Groups with operators were extensively studied by Emmy Noether and her school in the 1920s. She employed the concept in her original formulation of the three Noether isomorphism theorems.
Algebraic structures
Group-like
Group
Semigroup / Monoid
Rack and quandle
Quasigroup and loop
Abelian group
Magma
Lie group
Group theory
Ring-like
Ring
Rng
Semiring
Near-ring
Commutative ring
Domain
Integral domain
Field
Division ring
Lie ring
Ring theory
Lattice-like
Lattice
Semilattice
Complemented lattice
Total order
Heyting algebra
Boolean algebra
Map of lattices
Lattice theory
Module-like
Module
Group with operators
Vector space
Linear algebra
Algebra-like
Algebra
Associative
Non-associative
Composition algebra
Lie algebra
Graded
Bialgebra
Hopf algebra
v
t
e
and 19 Related for: Group with operators information
branch of mathematics, a groupwithoperators or Ω-group is an algebraic structure that can be viewed as a group together with a set Ω that operates on...
wh- interrogatives Operator (physics), mathematical operators in quantum physics Operator (band), an American hard rock band Operators, a synth pop band...
for example, groups have a signature containing two operators: the multiplication operator m, taking two arguments, and the inverse operator i, taking one...
List of Airbus A320neo family orders List of Boeing 737 operators List of Airbus A220 operators incl. Wizz Air Hungary, Wizz Air Malta, Wizz Air Abu Dhabi...
mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not...
Tour operators can sell directly to the public or sell through travel agents or a combination of both. The most common example of a tour operator's product...
semigroup of operators from X to itself, taking the initial state u0 at time t = 0 to the state u(t) = exp(tA)u0 at time t. The operator A is said to...
mobile phone operators, see Mobile country codes. This is a list of the world's thirty largest terrestrial mobile phone network operators measured by number...
particle with the creation/annihilation operators of QFT requires the use of both annihilation and creation operators. An annihilation operator is used...
present an asymmetric threat with a small group of operators, especially to South Korea. The earliest known attack that the group is responsible for is known...
octahedral group. Orbit of a fundamental spherical triangle (marked in red) under action of the full icosahedral group. Gain graph Groupwithoperators Measurable...
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study...
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical...
theory of concurrent computation. Out of the 16 possible binary Boolean operators, four have a two-sided identity that is also commutative and associative...
algebras of linear operators, for example on a Hilbert space. Here the algebra multiplication is given by the composition of operators. These algebras also...
into a larger force with expanded responsibilities and capabilities. It is now composed of nearly 1,000 operators: around 400 operators based in Satory,...
same reason, the Weyl algebra, and more general rings of differential operators, are Noetherian. The ring of polynomials in finitely-many variables over...
theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses....