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- Irreducible_component abstract "In mathematics, and specifically in algebraic geometry, the concept of irreducible component is used to make formal the idea that a set such as defined by the equationXY = 0is the union of the two linesX = 0and Y = 0.Thus an algebraic set is irreducible if it is not the union of two proper algebraic subsets. It is a fundamental theorem of classical algebraic geometry that every algebraic set is the union of a finite number of irreducible algebraic subsets (varieties) and that this decomposition is unique if one removes those subsets that are contained in another one. The elements of this unique decomposition are called irreducible components.This notion may be reformulated in topological terms, using Zariski topology, for which the closed sets are the subvarieties: an algebraic set is irreducible if it is not the union of two proper subsets that are closed for Zariski topology. This allows a generalization in topology, and, through it, to general schemes for which the above property of finite decomposition is not necessarily true.".
- Irreducible_component wikiPageID "2652476".
- Irreducible_component wikiPageLength "4456".
- Irreducible_component wikiPageOutDegree "36".
- Irreducible_component wikiPageRevisionID "679970875".
- Irreducible_component wikiPageWikiLink Affine_variety.
- Irreducible_component wikiPageWikiLink Algebraic_geometry.
- Irreducible_component wikiPageWikiLink Algebraic_set.
- Irreducible_component wikiPageWikiLink Algebraic_variety.
- Irreducible_component wikiPageWikiLink Category:Algebraic_geometry.
- Irreducible_component wikiPageWikiLink Category:Algebraic_varieties.
- Irreducible_component wikiPageWikiLink Category:General_topology.
- Irreducible_component wikiPageWikiLink Closed_set.
- Irreducible_component wikiPageWikiLink Closure_(topology).
- Irreducible_component wikiPageWikiLink Dense_set.
- Irreducible_component wikiPageWikiLink Field_(mathematics).
- Irreducible_component wikiPageWikiLink Hyperconnected_space.
- Irreducible_component wikiPageWikiLink Ideal_(ring_theory).
- Irreducible_component wikiPageWikiLink Intersection_(set_theory).
- Irreducible_component wikiPageWikiLink Mathematics.
- Irreducible_component wikiPageWikiLink Maximal_element.
- Irreducible_component wikiPageWikiLink Noetherian_scheme.
- Irreducible_component wikiPageWikiLink Open_set.
- Irreducible_component wikiPageWikiLink Polynomial_ring.
- Irreducible_component wikiPageWikiLink Primary_decomposition.
- Irreducible_component wikiPageWikiLink Prime_ideal.
- Irreducible_component wikiPageWikiLink Projective_variety.
- Irreducible_component wikiPageWikiLink Proper_subset.
- Irreducible_component wikiPageWikiLink Reduction_(mathematics).
- Irreducible_component wikiPageWikiLink Scheme_(mathematics).
- Irreducible_component wikiPageWikiLink Scheme_theory.
- Irreducible_component wikiPageWikiLink Singleton_(mathematics).
- Irreducible_component wikiPageWikiLink Subset.
- Irreducible_component wikiPageWikiLink Subspace_topology.
- Irreducible_component wikiPageWikiLink Topological_space.
- Irreducible_component wikiPageWikiLink Topological_spaces.
- Irreducible_component wikiPageWikiLink Topology.
- Irreducible_component wikiPageWikiLink Zariski_topology.
- Irreducible_component wikiPageWikiLinkText "Irreducible component".
- Irreducible_component wikiPageWikiLinkText "irreducible component".
- Irreducible_component wikiPageWikiLinkText "irreducible".
- Irreducible_component wikiPageWikiLinkText "reducible".
- Irreducible_component hasPhotoCollection Irreducible_component.
- Irreducible_component id "1109".
- Irreducible_component id "3107".
- Irreducible_component title "Irreducible component".
- Irreducible_component title "irreducible".
- Irreducible_component wikiPageUsesTemplate Template:PlanetMath_attribution.
- Irreducible_component subject Category:Algebraic_geometry.
- Irreducible_component subject Category:Algebraic_varieties.
- Irreducible_component subject Category:General_topology.
- Irreducible_component hypernym Union.
- Irreducible_component type Organisation.
- Irreducible_component type Source.
- Irreducible_component type Variety.
- Irreducible_component comment "In mathematics, and specifically in algebraic geometry, the concept of irreducible component is used to make formal the idea that a set such as defined by the equationXY = 0is the union of the two linesX = 0and Y = 0.Thus an algebraic set is irreducible if it is not the union of two proper algebraic subsets.".
- Irreducible_component label "Irreducible component".
- Irreducible_component sameAs Irreduzible_Varietät.
- Irreducible_component sameAs 既約成分.
- Irreducible_component sameAs m.07vjsf.
- Irreducible_component sameAs Q6073574.
- Irreducible_component sameAs Q6073574.
- Irreducible_component wasDerivedFrom Irreducible_component?oldid=679970875.
- Irreducible_component isPrimaryTopicOf Irreducible_component.