field adjunction
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Adjunction (field theory) — In abstract algebra, adjunction is a construction in field theory, where for a given field extension E / F , subextensions between E and F are constructed. Definition Let E be a field extension of a field F . Given a set of elements A in the… … Wikipedia
Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A … Wikipedia
Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… … Wikipedia
Canonical bundle — In mathematics, the canonical bundle of a non singular algebraic variety V of dimension n is the line bundle which is the nth exterior power of the cotangent bundle Ω on V. Over the complex numbers, it is the determinant bundle of holomorphic n… … Wikipedia
Tensor algebra — In mathematics, the tensor algebra of a vector space V , denoted T ( V ) or T bull;( V ), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V , in the sense of being left adjoint… … Wikipedia
Noether inequality — In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4 manifold. It holds more generally for minimal projective… … Wikipedia
Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia
Simple extension — In mathematics, more specifically in field theory, a simple extension is a field extension which is generated by the adjunction of a single element. Simple extensions are well understood and can be completely classified.The primitive element… … Wikipedia
Primitive element theorem — In mathematics, more specifically in field theory, the primitive element theorem provides a characterization of the finite field extensions which are simple and thus can be generated by the adjunction of a single primitive element. Primitive… … Wikipedia
