Separability may refer to:
Mathematics
*
Separable algebra
In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension.
Definition and First Properties
A ring homomorphism (of unital, but not necessari ...
, a generalization to associative algebras of the notion of a separable field extension
* Separable differential equation, in which
separation of variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs ...
is achieved by various means
*
Separable extension In field theory, a branch of algebra, an algebraic field extension E/F is called a separable extension if for every \alpha\in E, the minimal polynomial of \alpha over is a separable polynomial (i.e., its formal derivative is not the zero polynom ...
, in field theory, an algebraic field extension
*
Separable filter
Separability may refer to:
Mathematics
* Separable algebra, a generalization to associative algebras of the notion of a separable field extension
* Separable differential equation, in which separation of variables is achieved by various means
...
, a product of two or more simple filters in image processing
* Separable ordinary differential equation, a class of equations that can be
separated into a pair of integrals
*
Separable partial differential equation
A separable partial differential equation is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables. This generally relies upon the problem having some s ...
, a class of equations that can be broken down into differential equations in fewer independent variables
*
Separable permutation
In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums. Separable permutations may be characterized by the forbidden permutation patterns 2413 and 3 ...
, a permutation that can be obtained by direct sums and skew sums of the trivial permutation
*
Separable polynomial In mathematics, a polynomial ''P''(''X'') over a given field ''K'' is separable if its roots are distinct in an algebraic closure of ''K'', that is, the number of distinct roots is equal to the degree of the polynomial.
This concept is closely ...
, a polynomial whose number of distinct roots is equal to its degree
*
Separable sigma algebra
Separability may refer to:
Mathematics
* Separable algebra, a generalization to associative algebras of the notion of a separable field extension
* Separable differential equation, in which separation of variables is achieved by various means
...
, a separable space in measure theory
*
Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the ...
, a topological space that contains a countable, dense subset
*
Linear separability
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colo ...
, a geometric property of a pair of sets of points in Euclidean geometry
*
Recursively inseparable sets In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set.Monk 1976, p. 100 These sets arise in the study of computability the ...
, in computability theory, pairs of sets of natural numbers that cannot be "separated" with a recursive set
Other uses
*
Separable states
In quantum mechanics, separable states are quantum states belonging to a composite space that can be factored into individual states belonging to separate subspaces. A state is said to be entangled if it is not separable. In general, determinin ...
, in quantum mechanics, states without quantum entanglement
*
Separation process
A separation process is a method that converts a mixture or a solution of chemical substances into two or more distinct product mixtures, a scientific process of separating two or more substance in order to obtain purity. At least one product mi ...
, in chemistry, a method that converts a mixture of substances into two or more distinct product mixtures
{{disambiguation