Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Primary_decomposition> ?p ?o }
Showing triples 1 to 81 of
81
with 100 triples per page.
- Primary_decomposition abstract "In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by Emanuel Lasker (1905) for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by Emmy Noether (1921).The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The Lasker–Noether theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components.It has a straightforward extension to modules stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules. This contains the case for rings as a special case, considering the ring as a module over itself, so that ideals are submodules. This also generalizes the primary decomposition form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings over a field, it generalizes the decomposition of an algebraic set into a finite union of (irreducible) varieties.The first algorithm for computing primary decompositions for polynomial rings was published by Noether's student Grete Hermann (1926).".
- Primary_decomposition wikiPageExternalLink is-primary-decomposition-still-important.
- Primary_decomposition wikiPageExternalLink j57u808658262654.
- Primary_decomposition wikiPageExternalLink fulltext.pdf.
- Primary_decomposition wikiPageID "1208391".
- Primary_decomposition wikiPageLength "11226".
- Primary_decomposition wikiPageOutDegree "28".
- Primary_decomposition wikiPageRevisionID "669103058".
- Primary_decomposition wikiPageWikiLink Algebraic_geometry.
- Primary_decomposition wikiPageWikiLink Algebraic_set.
- Primary_decomposition wikiPageWikiLink Algebraic_variety.
- Primary_decomposition wikiPageWikiLink Associated_prime.
- Primary_decomposition wikiPageWikiLink Associated_prime_ideal.
- Primary_decomposition wikiPageWikiLink Category:Algebraic_geometry.
- Primary_decomposition wikiPageWikiLink Category:Commutative_algebra.
- Primary_decomposition wikiPageWikiLink Category:Theorems_in_abstract_algebra.
- Primary_decomposition wikiPageWikiLink Embedded_prime.
- Primary_decomposition wikiPageWikiLink Finitely_generated_abelian_group.
- Primary_decomposition wikiPageWikiLink Finitely_generated_module.
- Primary_decomposition wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Primary_decomposition wikiPageWikiLink Fundamental_theorem_of_finitely_generated_abelian_groups.
- Primary_decomposition wikiPageWikiLink Irreducible_component.
- Primary_decomposition wikiPageWikiLink Mathematics.
- Primary_decomposition wikiPageWikiLink Mathematische_Annalen.
- Primary_decomposition wikiPageWikiLink Module_(mathematics).
- Primary_decomposition wikiPageWikiLink Noetherian_ring.
- Primary_decomposition wikiPageWikiLink Polynomial_ring.
- Primary_decomposition wikiPageWikiLink Primary_ideal.
- Primary_decomposition wikiPageWikiLink Prime_ideal.
- Primary_decomposition wikiPageWikiLink Springer-Verlag.
- Primary_decomposition wikiPageWikiLink Springer_Science+Business_Media.
- Primary_decomposition wikiPageWikiLink Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain.
- Primary_decomposition wikiPageWikiLink Tertiary_ideal.
- Primary_decomposition wikiPageWikiLink Zero_divisor.
- Primary_decomposition wikiPageWikiLinkText "Primary decomposition".
- Primary_decomposition wikiPageWikiLinkText "primary decomposition".
- Primary_decomposition authorlink "Emanuel Lasker".
- Primary_decomposition authorlink "Emmy Noether".
- Primary_decomposition authorlink "Grete Hermann".
- Primary_decomposition first "Emanuel".
- Primary_decomposition first "Emmy".
- Primary_decomposition first "Grete".
- Primary_decomposition first "V.I.".
- Primary_decomposition first "V.T.".
- Primary_decomposition hasPhotoCollection Primary_decomposition.
- Primary_decomposition id "L/l057600".
- Primary_decomposition id "P/p074450".
- Primary_decomposition last "Danilov".
- Primary_decomposition last "Hermann".
- Primary_decomposition last "Lasker".
- Primary_decomposition last "Markov".
- Primary_decomposition last "Noether".
- Primary_decomposition title "Lasker ring".
- Primary_decomposition title "Primary decomposition".
- Primary_decomposition wikiPageUsesTemplate Template:Citation.
- Primary_decomposition wikiPageUsesTemplate Template:Harvs.
- Primary_decomposition wikiPageUsesTemplate Template:Reflist.
- Primary_decomposition wikiPageUsesTemplate Template:Springer.
- Primary_decomposition year "1905".
- Primary_decomposition year "1921".
- Primary_decomposition year "1926".
- Primary_decomposition subject Category:Algebraic_geometry.
- Primary_decomposition subject Category:Commutative_algebra.
- Primary_decomposition subject Category:Theorems_in_abstract_algebra.
- Primary_decomposition hypernym Ring.
- Primary_decomposition type AnatomicalStructure.
- Primary_decomposition comment "In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals).".
- Primary_decomposition label "Primary decomposition".
- Primary_decomposition sameAs Primärzerlegung.
- Primary_decomposition sameAs Décomposition_primaire.
- Primary_decomposition sameAs משפט_לסקר-נתר.
- Primary_decomposition sameAs Decomposizione_primaria.
- Primary_decomposition sameAs 으뜸_분해.
- Primary_decomposition sameAs Stelling_van_Lasker-Noether.
- Primary_decomposition sameAs m.04hcj6.
- Primary_decomposition sameAs Теорема_Ласкера_—_Нётер.
- Primary_decomposition sameAs Q172298.
- Primary_decomposition sameAs Q172298.
- Primary_decomposition sameAs 準素分解.
- Primary_decomposition wasDerivedFrom Primary_decomposition?oldid=669103058.
- Primary_decomposition isPrimaryTopicOf Primary_decomposition.