Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Unit_(ring_theory)> ?p ?o }
- Unit_(ring_theory) abstract "In mathematics, an invertible element or a unit in a (unital) ring R is any element u that has an inverse element in the multiplicative monoid of R, i.e. an element v such thatuv = vu = 1R, where 1R is the multiplicative identity.The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation. It never contains the element 0 (except in the case of the zero ring), and is therefore not closed under addition; its complement however might be a group under addition, which happens if and only if the ring is a local ring.The term unit is also used to refer to the identity element 1R of the ring, in expressions like ring with a unit or unit ring, and also e.g. 'unit' matrix. For this reason, some authors call 1R "unity" or "identity", and say that R is a "ring with unity" or a "ring with identity" rather than a "ring with a unit".The multiplicative identity 1R and its opposite −1R are always units. Hence, pairs of additive inverse elements x and −x are always associated.".
- Unit_(ring_theory) wikiPageID "289666".
- Unit_(ring_theory) wikiPageLength "5138".
- Unit_(ring_theory) wikiPageOutDegree "53".
- Unit_(ring_theory) wikiPageRevisionID "676359163".
- Unit_(ring_theory) wikiPageWikiLink 1_(number).
- Unit_(ring_theory) wikiPageWikiLink Additive_identity.
- Unit_(ring_theory) wikiPageWikiLink Additive_inverse.
- Unit_(ring_theory) wikiPageWikiLink Adjoint_functors.
- Unit_(ring_theory) wikiPageWikiLink Algebra_over_a_field.
- Unit_(ring_theory) wikiPageWikiLink Algebraic_number_field.
- Unit_(ring_theory) wikiPageWikiLink Associated_element.
- Unit_(ring_theory) wikiPageWikiLink Cardinality.
- Unit_(ring_theory) wikiPageWikiLink Category:1_(number).
- Unit_(ring_theory) wikiPageWikiLink Category:Algebraic_number_theory.
- Unit_(ring_theory) wikiPageWikiLink Category:Group_theory.
- Unit_(ring_theory) wikiPageWikiLink Category:Ring_theory.
- Unit_(ring_theory) wikiPageWikiLink Category_of_groups.
- Unit_(ring_theory) wikiPageWikiLink Category_of_rings.
- Unit_(ring_theory) wikiPageWikiLink Complement_(set_theory).
- Unit_(ring_theory) wikiPageWikiLink Coprime.
- Unit_(ring_theory) wikiPageWikiLink Coprime_integers.
- Unit_(ring_theory) wikiPageWikiLink Dirichlets_unit_theorem.
- Unit_(ring_theory) wikiPageWikiLink Division_ring.
- Unit_(ring_theory) wikiPageWikiLink Equivalence_relation.
- Unit_(ring_theory) wikiPageWikiLink Field_(mathematics).
- Unit_(ring_theory) wikiPageWikiLink Finitely_generated_abelian_group.
- Unit_(ring_theory) wikiPageWikiLink Functor.
- Unit_(ring_theory) wikiPageWikiLink General_linear_group.
- Unit_(ring_theory) wikiPageWikiLink Group_(mathematics).
- Unit_(ring_theory) wikiPageWikiLink Group_action.
- Unit_(ring_theory) wikiPageWikiLink Group_homomorphism.
- Unit_(ring_theory) wikiPageWikiLink Group_ring.
- Unit_(ring_theory) wikiPageWikiLink Identity_matrix.
- Unit_(ring_theory) wikiPageWikiLink If_and_only_if.
- Unit_(ring_theory) wikiPageWikiLink Integer.
- Unit_(ring_theory) wikiPageWikiLink Integers.
- Unit_(ring_theory) wikiPageWikiLink Integral_domain.
- Unit_(ring_theory) wikiPageWikiLink Inverse_element.
- Unit_(ring_theory) wikiPageWikiLink Invertible_matrix.
- Unit_(ring_theory) wikiPageWikiLink Left_adjoint.
- Unit_(ring_theory) wikiPageWikiLink Local_ring.
- Unit_(ring_theory) wikiPageWikiLink Mathematics.
- Unit_(ring_theory) wikiPageWikiLink Modular_arithmetic.
- Unit_(ring_theory) wikiPageWikiLink Monoid.
- Unit_(ring_theory) wikiPageWikiLink Multiplication.
- Unit_(ring_theory) wikiPageWikiLink Multiplicative_group_of_integers_modulo_n.
- Unit_(ring_theory) wikiPageWikiLink Multiplicative_identity.
- Unit_(ring_theory) wikiPageWikiLink Number_field.
- Unit_(ring_theory) wikiPageWikiLink Orbit_(group_theory).
- Unit_(ring_theory) wikiPageWikiLink Quadratic_field.
- Unit_(ring_theory) wikiPageWikiLink Quadratic_integer.
- Unit_(ring_theory) wikiPageWikiLink Real_quadratic_field.
- Unit_(ring_theory) wikiPageWikiLink Ring_(algebra).
- Unit_(ring_theory) wikiPageWikiLink Ring_(mathematics).
- Unit_(ring_theory) wikiPageWikiLink Ring_homomorphism.
- Unit_(ring_theory) wikiPageWikiLink Ring_of_integers.
- Unit_(ring_theory) wikiPageWikiLink Root_of_unity.
- Unit_(ring_theory) wikiPageWikiLink Square_matrix.
- Unit_(ring_theory) wikiPageWikiLink Unit_ring.
- Unit_(ring_theory) wikiPageWikiLink Unital_algebra.
- Unit_(ring_theory) wikiPageWikiLink Wikt:Einheit.
- Unit_(ring_theory) wikiPageWikiLink Zero_ring.
- Unit_(ring_theory) wikiPageWikiLinkText "Unit (ring theory)".
- Unit_(ring_theory) wikiPageWikiLinkText "Unit (ring theory)#Group of units".
- Unit_(ring_theory) wikiPageWikiLinkText "Unit".
- Unit_(ring_theory) wikiPageWikiLinkText "associate".
- Unit_(ring_theory) wikiPageWikiLinkText "associates".
- Unit_(ring_theory) wikiPageWikiLinkText "comes from ring theory".
- Unit_(ring_theory) wikiPageWikiLinkText "group of units".
- Unit_(ring_theory) wikiPageWikiLinkText "invertible element".
- Unit_(ring_theory) wikiPageWikiLinkText "invertible elements".
- Unit_(ring_theory) wikiPageWikiLinkText "invertible".
- Unit_(ring_theory) wikiPageWikiLinkText "non-unit".
- Unit_(ring_theory) wikiPageWikiLinkText "unit (ring theory)".
- Unit_(ring_theory) wikiPageWikiLinkText "unit group".
- Unit_(ring_theory) wikiPageWikiLinkText "unit groups".
- Unit_(ring_theory) wikiPageWikiLinkText "unit".
- Unit_(ring_theory) wikiPageWikiLinkText "units".
- Unit_(ring_theory) wikiPageWikiLinkText "with unity".
- Unit_(ring_theory) hasPhotoCollection Unit_(ring_theory).
- Unit_(ring_theory) wikiPageUsesTemplate Template:Anchor.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Distinguish.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Main.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Math.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Mvar.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Reflist.
- Unit_(ring_theory) wikiPageUsesTemplate Template:Visible_anchor.
- Unit_(ring_theory) subject Category:1_(number).
- Unit_(ring_theory) subject Category:Algebraic_number_theory.
- Unit_(ring_theory) subject Category:Group_theory.
- Unit_(ring_theory) subject Category:Ring_theory.
- Unit_(ring_theory) hypernym Identity.
- Unit_(ring_theory) type Person.
- Unit_(ring_theory) type Thing.
- Unit_(ring_theory) comment "In mathematics, an invertible element or a unit in a (unital) ring R is any element u that has an inverse element in the multiplicative monoid of R, i.e. an element v such thatuv = vu = 1R, where 1R is the multiplicative identity.The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.".
- Unit_(ring_theory) label "Unit (ring theory)".
- Unit_(ring_theory) differentFrom Ring_(mathematics).
- Unit_(ring_theory) sameAs وحدة_(نظرية_الحلقات).
- Unit_(ring_theory) sameAs Element_invertible.