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- Division_ring abstract "In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring in which every nonzero element a has a multiplicative inverse, i.e., an element x with a·x = x·a = 1. Stated differently, a ring is a division ring if and only if the group of units equals the set of all nonzero elements.Division rings differ from fields only in that their multiplication is not required to be commutative. However, by Wedderburn's little theorem all finite division rings are commutative and therefore finite fields. Historically, division rings were sometimes referred to as fields, while fields were called “commutative fields”.".
- Division_ring wikiPageExternalLink every-r-module-is-free-implies-r-is-a-division-ring.
- Division_ring wikiPageExternalLink ?op=getobj&from=objects&id=3627.
- Division_ring wikiPageID "9067".
- Division_ring wikiPageLength "8429".
- Division_ring wikiPageOutDegree "53".
- Division_ring wikiPageRevisionID "664216891".
- Division_ring wikiPageWikiLink Abstract_algebra.
- Division_ring wikiPageWikiLink Automorphism.
- Division_ring wikiPageWikiLink Cambridge_University_Press.
- Division_ring wikiPageWikiLink Category:Ring_theory.
- Division_ring wikiPageWikiLink Center_(algebra).
- Division_ring wikiPageWikiLink Center_of_a_ring.
- Division_ring wikiPageWikiLink Commutative.
- Division_ring wikiPageWikiLink Commutative_property.
- Division_ring wikiPageWikiLink Complex_conjugate.
- Division_ring wikiPageWikiLink Complex_number.
- Division_ring wikiPageWikiLink Distributive_law.
- Division_ring wikiPageWikiLink Distributive_property.
- Division_ring wikiPageWikiLink Division_(mathematics).
- Division_ring wikiPageWikiLink Division_algebra.
- Division_ring wikiPageWikiLink Endomorphism_ring.
- Division_ring wikiPageWikiLink Ernst_Witt.
- Division_ring wikiPageWikiLink Field_(mathematics).
- Division_ring wikiPageWikiLink Finite_field.
- Division_ring wikiPageWikiLink Formal_Laurent_series.
- Division_ring wikiPageWikiLink Formal_power_series.
- Division_ring wikiPageWikiLink Free_module.
- Division_ring wikiPageWikiLink Frobenius_theorem_(real_division_algebras).
- Division_ring wikiPageWikiLink Gaussian_elimination.
- Division_ring wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Division_ring wikiPageWikiLink Group_of_units.
- Division_ring wikiPageWikiLink Hamiltonian_quaternions.
- Division_ring wikiPageWikiLink Huas_identity.
- Division_ring wikiPageWikiLink Identity_function.
- Division_ring wikiPageWikiLink Lexical_semantics.
- Division_ring wikiPageWikiLink Linear_algebra.
- Division_ring wikiPageWikiLink Matrix_(mathematics).
- Division_ring wikiPageWikiLink Module_(mathematics).
- Division_ring wikiPageWikiLink Multiplicative_inverse.
- Division_ring wikiPageWikiLink Near-field_(mathematics).
- Division_ring wikiPageWikiLink Octonion.
- Division_ring wikiPageWikiLink Quaternion.
- Division_ring wikiPageWikiLink Rational_number.
- Division_ring wikiPageWikiLink Real_number.
- Division_ring wikiPageWikiLink Ring_(mathematics).
- Division_ring wikiPageWikiLink Ring_of_formal_Laurent_series.
- Division_ring wikiPageWikiLink Schurs_lemma.
- Division_ring wikiPageWikiLink Simple_module.
- Division_ring wikiPageWikiLink Unit_(ring_theory).
- Division_ring wikiPageWikiLink Vector_space.
- Division_ring wikiPageWikiLink Wedderburns_little_theorem.
- Division_ring wikiPageWikiLink Zero_ring.
- Division_ring wikiPageWikiLinkText "(skew) field".
- Division_ring wikiPageWikiLinkText "Division ring".
- Division_ring wikiPageWikiLinkText "Wedderburn's theorem (division ring)".
- Division_ring wikiPageWikiLinkText "division ring".
- Division_ring wikiPageWikiLinkText "skew-field".
- Division_ring wikiPageWikiLinkText "strictly skew field".
- Division_ring hasPhotoCollection Division_ring.
- Division_ring wikiPageUsesTemplate Template:Cite_book.
- Division_ring wikiPageUsesTemplate Template:Math.
- Division_ring subject Category:Ring_theory.
- Division_ring hypernym Ring.
- Division_ring type AnatomicalStructure.
- Division_ring comment "In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring in which every nonzero element a has a multiplicative inverse, i.e., an element x with a·x = x·a = 1. Stated differently, a ring is a division ring if and only if the group of units equals the set of all nonzero elements.Division rings differ from fields only in that their multiplication is not required to be commutative.".
- Division_ring label "Division ring".
- Division_ring sameAs Těleso_(algebra).
- Division_ring sameAs Schiefkörper.
- Division_ring sameAs Korpo_(algebro).
- Division_ring sameAs Anillo_de_división.
- Division_ring sameAs Kaldkorpus.
- Division_ring sameAs Corps_(mathématiques).
- Division_ring sameAs חוג_עם_חילוק.
- Division_ring sameAs Ferdetest.
- Division_ring sameAs Corpo_(matematica).
- Division_ring sameAs 斜体_(数学).
- Division_ring sameAs 나눗셈환.
- Division_ring sameAs _Lichaam_(Be).
- Division_ring sameAs Pierścień_z_dzieleniem.
- Division_ring sameAs m.02hj_.
- Division_ring sameAs Тело_(алгебра).
- Division_ring sameAs Corpu_(matimàtica).
- Division_ring sameAs Obseg_(algebra).
- Division_ring sameAs Skevkropp.
- Division_ring sameAs Тіло_(алгебра).
- Division_ring sameAs Q650741.
- Division_ring sameAs Q650741.
- Division_ring sameAs 除环.
- Division_ring wasDerivedFrom Division_ring?oldid=664216891.
- Division_ring isPrimaryTopicOf Division_ring.