DBpedia – Linked Data Fragments

Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Nakayama_lemma> ?p ?o }

• Nakayama_lemma abstract "In mathematics, more specifically modern algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring.The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in Nakayama (1951), although it was first discovered in the special case of ideals in a commutative ring by Wolfgang Krull and then in general by Goro Azumaya (1951). In the commutative case, the lemma is a simple consequence of a generalized form of the Cayley–Hamilton theorem, an observation made by Michael Atiyah (1969). The special case of the noncommutative version of the lemma for right ideals appears in Nathan Jacobson (1945), and so the noncommutative Nakayama lemma is sometimes known as the Jacobson–Azumaya theorem. The latter has various applications in the theory of Jacobson radicals.".
• Nakayama_lemma wikiPageID "1835001".
• Nakayama_lemma wikiPageLength "18057".
• Nakayama_lemma wikiPageOutDegree "73".
• Nakayama_lemma wikiPageRevisionID "683414224".
• Nakayama_lemma wikiPageWikiLink Abstract_algebra.
• Nakayama_lemma wikiPageWikiLink Algebraic_geometry.
• Nakayama_lemma wikiPageWikiLink Algebraic_variety.
• Nakayama_lemma wikiPageWikiLink American_Journal_of_Mathematics.
• Nakayama_lemma wikiPageWikiLink Basis_(linear_algebra).
• Nakayama_lemma wikiPageWikiLink Basis_of_a_vector_space.
• Nakayama_lemma wikiPageWikiLink Cambridge_University_Press.
• Nakayama_lemma wikiPageWikiLink Category:Algebraic_geometry.
• Nakayama_lemma wikiPageWikiLink Category:Commutative_algebra.
• Nakayama_lemma wikiPageWikiLink Category:Lemmas.
• Nakayama_lemma wikiPageWikiLink Category:Theorems_in_abstract_algebra.
• Nakayama_lemma wikiPageWikiLink Cayley–Hamilton_theorem.
• Nakayama_lemma wikiPageWikiLink Cofactor_(linear_algebra).
• Nakayama_lemma wikiPageWikiLink Coherent_sheaf.
• Nakayama_lemma wikiPageWikiLink Commutative_algebra.
• Nakayama_lemma wikiPageWikiLink Commutative_ring.
• Nakayama_lemma wikiPageWikiLink Compact_set.
• Nakayama_lemma wikiPageWikiLink Compact_space.
• Nakayama_lemma wikiPageWikiLink Completion_(algebra).
• Nakayama_lemma wikiPageWikiLink Completion_(ring_theory).
• Nakayama_lemma wikiPageWikiLink Cramers_rule.
• Nakayama_lemma wikiPageWikiLink Field_(mathematics).
• Nakayama_lemma wikiPageWikiLink Finitely-generated_module.
• Nakayama_lemma wikiPageWikiLink Finitely_generated_module.
• Nakayama_lemma wikiPageWikiLink Free_module.
• Nakayama_lemma wikiPageWikiLink Free_resolution.
• Nakayama_lemma wikiPageWikiLink Germ_(mathematics).
• Nakayama_lemma wikiPageWikiLink Goro_Azumaya.
• Nakayama_lemma wikiPageWikiLink Graded_ring.
• Nakayama_lemma wikiPageWikiLink Homological_algebra.
• Nakayama_lemma wikiPageWikiLink Ideal_(ring_theory).
• Nakayama_lemma wikiPageWikiLink Integral_element.
• Nakayama_lemma wikiPageWikiLink Integral_extension.
• Nakayama_lemma wikiPageWikiLink Invertible_matrix.
• Nakayama_lemma wikiPageWikiLink Jacobson_radical.
• Nakayama_lemma wikiPageWikiLink John_Wiley_&_Sons.
• Nakayama_lemma wikiPageWikiLink Local_ring.
• Nakayama_lemma wikiPageWikiLink Mathematician.
• Nakayama_lemma wikiPageWikiLink Mathematics.
• Nakayama_lemma wikiPageWikiLink Maximal_ideal.
• Nakayama_lemma wikiPageWikiLink Maximal_submodule.
• Nakayama_lemma wikiPageWikiLink Michael_Atiyah.
• Nakayama_lemma wikiPageWikiLink Minor_(linear_algebra).
• Nakayama_lemma wikiPageWikiLink Module_(mathematics).
• Nakayama_lemma wikiPageWikiLink Module_theory.
• Nakayama_lemma wikiPageWikiLink Monic_polynomial.
• Nakayama_lemma wikiPageWikiLink Nathan_Jacobson.
• Nakayama_lemma wikiPageWikiLink Noetherian_ring.
• Nakayama_lemma wikiPageWikiLink Prime_ideal.
• Nakayama_lemma wikiPageWikiLink Projective_dimension.
• Nakayama_lemma wikiPageWikiLink Projective_module.
• Nakayama_lemma wikiPageWikiLink Proper_map.
• Nakayama_lemma wikiPageWikiLink Quasiregular_element.
• Nakayama_lemma wikiPageWikiLink Resolution_(algebra).
• Nakayama_lemma wikiPageWikiLink Ring_(mathematics).
• Nakayama_lemma wikiPageWikiLink Scheme_(mathematics).
• Nakayama_lemma wikiPageWikiLink Section_(fiber_bundle).
• Nakayama_lemma wikiPageWikiLink Serre–Swan_theorem.
• Nakayama_lemma wikiPageWikiLink Simple_module.
• Nakayama_lemma wikiPageWikiLink Springer-Verlag.
• Nakayama_lemma wikiPageWikiLink Springer_Science+Business_Media.
• Nakayama_lemma wikiPageWikiLink Stalk_(mathematics).
• Nakayama_lemma wikiPageWikiLink Stalk_(sheaf).
• Nakayama_lemma wikiPageWikiLink T1_space.
• Nakayama_lemma wikiPageWikiLink Tadashi_Nakayama_(mathematician).
• Nakayama_lemma wikiPageWikiLink Tor_functor.
• Nakayama_lemma wikiPageWikiLink Unit_(ring_theory).
• Nakayama_lemma wikiPageWikiLink Unitary_ring.
• Nakayama_lemma wikiPageWikiLink Vector_bundle.
• Nakayama_lemma wikiPageWikiLink Vector_space.
• Nakayama_lemma wikiPageWikiLink Wolfgang_Krull.
• Nakayama_lemma wikiPageWikiLinkText "Nakayama lemma".
• Nakayama_lemma wikiPageWikiLinkText "nakayama lemma".
• Nakayama_lemma hasPhotoCollection Nakayama_lemma.
• Nakayama_lemma wikiPageUsesTemplate Template:Citation.
• Nakayama_lemma wikiPageUsesTemplate Template:Harvtxt.
• Nakayama_lemma wikiPageUsesTemplate Template:Main.
• Nakayama_lemma wikiPageUsesTemplate Template:Reflist.
• Nakayama_lemma subject Category:Algebraic_geometry.
• Nakayama_lemma subject Category:Commutative_algebra.
• Nakayama_lemma subject Category:Lemmas.
• Nakayama_lemma subject Category:Theorems_in_abstract_algebra.
• Nakayama_lemma type Article.
• Nakayama_lemma type Article.
• Nakayama_lemma type Lemma.
• Nakayama_lemma type Theorem.
• Nakayama_lemma comment "In mathematics, more specifically modern algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field.".
• Nakayama_lemma label "Nakayama lemma".
• Nakayama_lemma sameAs Lemma_von_Nakayama.
• Nakayama_lemma sameAs Lemma_von_Nakayama.
• Nakayama_lemma sameAs Nakajaman_lemma.
• Nakayama_lemma sameAs Lemme_de_Nakayama.
• Nakayama_lemma sameAs הלמה_של_נקאימה.
• Nakayama_lemma sameAs Lemma_di_Nakayama.
• Nakayama_lemma sameAs 中山の補題.

• next