About: Dimension of an algebraic variety

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In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding.

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rdfs:label	Dimension of an algebraic variety (en) Dimensão de uma variedade algébrica (pt)
rdfs:comment	In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding. (en) Em matemática, a dimensão de uma variedade algébrica V em geometria algébrica é definida, informalmente falando, como o número de funções racionais independentes que existem em V. Por exemplo, uma curva algébrica tem por definição dimensão 1. Isto significa que dadas quaisquer duas funções racionais F e G, sobre elas deve-se satisfazer alguma relação polinomial Isto implica que F e G estão delimitadas a terem valores relacionados (até alguma finita liberdade de escolha): eles não podem ser verdadeiramente independentes. (pt)
rdfs:seeAlso	Complex dimension
dcterms:subject	Algebraic varieties Dimension Computer algebra
Wikipage page ID	253251 (xsd:integer)
Wikipage revision ID	999655356 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime ideal Projective space Semialgebraic set Algebraic set Algebraic surface Algebraic varieties Vector space Mathematics General position Graded algebra Macaulay2 Commutative algebra Computer algebra system Zariski closure Zariski tangent space Krull dimension Tangent space Local ring Affine space Algebraic geometry Algebraic variety Euclidean space Field (mathematics) Dimension of a scheme Radical of an ideal Dimension Gröbner basis Hyperplane Hypersurface Computer algebra System of polynomial equations Homeomorphism Zero of a function Regular sequence Differentiable manifold Dimension theory (algebra) Manifold Maple (software) Field of fractions Interior (topology) Real number Stanley–Reisner ring Singular point of an algebraic variety Transcendence degree Affine algebraic set Projective algebraic set Birational equivalence Hilbert polynomial Hilbert series
sameAs	Dimension of an algebraic variety Dimension of an algebraic variety Dimension of an algebraic variety Dimension of an algebraic variety Dimension of an algebraic variety Dimension of an algebraic variety
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has abstract	In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding. (en) Em matemática, a dimensão de uma variedade algébrica V em geometria algébrica é definida, informalmente falando, como o número de funções racionais independentes que existem em V. Por exemplo, uma curva algébrica tem por definição dimensão 1. Isto significa que dadas quaisquer duas funções racionais F e G, sobre elas deve-se satisfazer alguma relação polinomial Isto implica que F e G estão delimitadas a terem valores relacionados (até alguma finita liberdade de escolha): eles não podem ser verdadeiramente independentes. (pt)
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page length (characters) of wiki page	10050 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Dimension_of_an_algebraic_variety
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics Multiplicity (mathematics) Norm variety Rational variety Algebraic surface Resultant Curve Degree of an algebraic variety Geometry Glossary of algebraic geometry Branched covering Thin set (Serre) Stable group Underdetermined system Complete intersection Complete variety Complex dimension

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