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  • late 14c., from Latin separabilis, from separare (see separate (v.)). Related: Separability.

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  • Separable extension In field theory, a subfield of algebra, a separable extension is an algebraic field extension such that for every , the minimal polynomial of over F is a separable polynomial. Otherwise, the extension is said to be inseparable.
  • 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 sequence.
  • 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.
  • Separable verb A separable verb is a verb that is composed of a lexical core and a separable particle. In some sentence positions, the core verb and the particle appear in one word, whilst in others the core verb and the particle are separated. The particle cannot be accurately referred to as a prefix because it can be separated from the core verb. German, Dutch, Afrikaans and Hungarian are notable for having many separable verbs. Separable verbs challenge theories of sentence structure because when they are separated, it is not evident how the compositionality of meaning should be understood.
  • Separable partial differential equation A separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality by a method of separation of variables. This generally relies upon the problem having some special form or symmetry. In this way, the PDE can be solved by solving a set of simpler PDEs, or even ordinary differential equations (ODEs) if the problem can be broken down into one-dimensional equations.
  • 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.
  • Separable filter A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into two 1-dimensional filters. This reduces the cost of computing the operator.
  • Separable state In quantum mechanics, separable quantum states are states without quantum entanglement.
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