Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Primary_decomposition> ?p ?o. }
Showing items 1 to 43 of
43
with 100 items 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 written as an intersection 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 j57u808658262654.
- Primary_decomposition wikiPageExternalLink fulltext.pdf.
- Primary_decomposition wikiPageID "1208391".
- Primary_decomposition wikiPageRevisionID "594615575".
- 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 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 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 comment "In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be written as an intersection of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals).".
- Primary_decomposition label "Décomposition primaire".
- Primary_decomposition label "Primary decomposition".
- Primary_decomposition label "Primärzerlegung".
- Primary_decomposition label "Stelling van Lasker-Noether".
- Primary_decomposition label "Теорема Ласкера — Нётер".
- Primary_decomposition label "準素分解".
- Primary_decomposition sameAs Primärzerlegung.
- Primary_decomposition sameAs Décomposition_primaire.
- Primary_decomposition sameAs Stelling_van_Lasker-Noether.
- Primary_decomposition sameAs m.04hcj6.
- Primary_decomposition sameAs Q172298.
- Primary_decomposition sameAs Q172298.
- Primary_decomposition wasDerivedFrom Primary_decomposition?oldid=594615575.
- Primary_decomposition isPrimaryTopicOf Primary_decomposition.