Normal closure

Normal closure

The term normal closure is used in two senses in mathematics:


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  • Normal extension — In abstract algebra, an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X]. Bourbaki calls such an extension a quasi Galois extension. Contents 1 Equivalent properties and examples 2… …   Wikipedia

  • Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …   Wikipedia

  • Normal scheme — In mathematics, in the field of algebraic geometry, a normal scheme is a scheme X for which every stalk (local ring) OX,x of its structure sheaf OX is an integrally closed local ring; that is, each stalk is an integral domain such that its… …   Wikipedia

  • Normal subgroup — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

  • Normal (mathematics) — In mathematics, normal can have several meanings:* Surface normal, a vector (or line) that is perpendicular to a surface. * Normal component, the component of a vector that is perpendicular to a surface. ** Normal curvature, of a curve on a… …   Wikipedia

  • Conjugate closure — In group theory, the conjugate closure of a subset S of a group G is the subgroup of G generated by SG, i.e. the closure of SG under the group operation, where SG is the conjugates of the elements of S: SG = {g−1sg | g ∈ G and s ∈ S} The… …   Wikipedia

  • Angle-closure glaucoma — This condition can be acute or chronic. It consists of increased pressure in the front chamber (anterior chamber) of the eye due to sudden (acute) or slowly progressive (chronic) blockage of the normal circulation of fluid within the eye. The… …   Medical dictionary

  • Glaucoma, angle-closure — Increased pressure in the front chamber (anterior chamber) of the eye due to sudden (acute) or slowly progressive (chronic) blockage of the normal circulation of fluid within the eye. The block takes place at the angle of the anterior chamber… …   Medical dictionary

  • Acute angle-closure glaucoma — Increased pressure in the front chamber (anterior chamber) of the eye due to sudden (acute) blockage of the normal circulation of fluid within the eye. The block takes place at the angle of the anterior chamber formed by its junction of the… …   Medical dictionary

  • Angle-closure glaucoma, acute — Increased pressure in the front chamber (anterior chamber) of the eye due to sudden (acute) blockage of the normal circulation of fluid within the eye. The block takes place at the angle of the anterior chamber formed by its junction of the… …   Medical dictionary

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