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- Simple_ring abstract "In abstract algebra, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. A simple ring can always be considered as a simple algebra. Rings which are simple as rings but not as modules do exist: the full matrix ring over a field does not have any nontrivial ideals (since any ideal of M(n,R) is of the form M(n,I) with I an ideal of R), but has nontrivial left ideals (namely, the sets of matrices which have some fixed zero columns).According to the Artin–Wedderburn theorem, every simple ring that is left or right Artinian is a matrix ring over a division ring. In particular, the only simple rings that are a finite-dimensional vector space over the real numbers are rings of matrices over either the real numbers, the complex numbers, or the quaternions.Any quotient of a ring by a maximal ideal is a simple ring. In particular, a field is a simple ring. A ring R is simple if and only its opposite ring Ro is simple.An example of a simple ring that is not a matrix ring over a division ring is the Weyl algebra.".
- Simple_ring wikiPageID "443387".
- Simple_ring wikiPageLength "4569".
- Simple_ring wikiPageOutDegree "24".
- Simple_ring wikiPageRevisionID "627082294".
- Simple_ring wikiPageWikiLink Abstract_algebra.
- Simple_ring wikiPageWikiLink Artinian_ring.
- Simple_ring wikiPageWikiLink Artin–Wedderburn_theorem.
- Simple_ring wikiPageWikiLink Category:Ring_theory.
- Simple_ring wikiPageWikiLink Complex_number.
- Simple_ring wikiPageWikiLink Division_ring.
- Simple_ring wikiPageWikiLink Field_(mathematics).
- Simple_ring wikiPageWikiLink Ideal_(ring_theory).
- Simple_ring wikiPageWikiLink Isomorphism.
- Simple_ring wikiPageWikiLink Matrix_ring.
- Simple_ring wikiPageWikiLink Maximal_ideal.
- Simple_ring wikiPageWikiLink Module_(mathematics).
- Simple_ring wikiPageWikiLink Opposite_ring.
- Simple_ring wikiPageWikiLink Quaternion.
- Simple_ring wikiPageWikiLink Real_number.
- Simple_ring wikiPageWikiLink Ring_(mathematics).
- Simple_ring wikiPageWikiLink Simple_(abstract_algebra).
- Simple_ring wikiPageWikiLink Simple_algebra.
- Simple_ring wikiPageWikiLink Springer_Science+Business_Media.
- Simple_ring wikiPageWikiLink Vector_space.
- Simple_ring wikiPageWikiLink Weyl_algebra.
- Simple_ring wikiPageWikiLink Zero_element.
- Simple_ring wikiPageWikiLinkText "Simple ring".
- Simple_ring wikiPageWikiLinkText "Wedderburn's theorem (simple ring)".
- Simple_ring wikiPageWikiLinkText "simple ring".
- Simple_ring wikiPageWikiLinkText "simple".
- Simple_ring wikiPageUsesTemplate Template:Citation.
- Simple_ring subject Category:Ring_theory.
- Simple_ring hypernym Ring.
- Simple_ring type AnatomicalStructure.
- Simple_ring comment "In abstract algebra, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. A simple ring can always be considered as a simple algebra.".
- Simple_ring label "Simple ring".
- Simple_ring sameAs Q2326800.
- Simple_ring sameAs Jednoduchý_okruh.
- Simple_ring sameAs Anneau_simple.
- Simple_ring sameAs חוג_פשוט.
- Simple_ring sameAs Anello_semplice.
- Simple_ring sameAs 単純環.
- Simple_ring sameAs 단순환.
- Simple_ring sameAs Enkelvoudige_ring.
- Simple_ring sameAs m.02946p.
- Simple_ring sameAs Простое_кольцо_(алгебра).
- Simple_ring sameAs Просте_кільце.
- Simple_ring sameAs Q2326800.
- Simple_ring wasDerivedFrom Simple_ring?oldid=627082294.
- Simple_ring isPrimaryTopicOf Simple_ring.