Von Neumann regular ring
In mathematics, a von Neumann regular ring is a ring R (associative, with 1, not necessarily commutative) such that for every element a in R there exists an x in R with a = axa. One may think of x as a "weak inverse" of the element a; in general x is not uniquely determined by a. Von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left R-module is flat.
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Absolutely-flat ringAbsolutely flatAbsolutely flat ringAffiliated operatorBaer ringBoolean ringCongruence lattice problemConstructible topologyContinuous geometryDedekind-infinite setDimension theory (algebra)Endomorphism ringFlat moduleGlossary of commutative algebraGlossary of ring theoryHereditary ringIdempotent (ring theory)Jacobson radicalJohn_von_NeumannKrull dimensionList of abstract algebra topicsList of things named after John von NeumannMoore–Penrose inverseMorita equivalencePrimitive ringPrincipal ideal ringPure submoduleRadical of a ringRank ringReal closed ringRefinement monoidRegularRegular elementRegular idealRegular local ringRegular ring (in the sense of von Neumann)Resolution (algebra)Semiprimitive ringSemisimple moduleSingular submodule
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Von Neumann regular ring
In mathematics, a von Neumann regular ring is a ring R (associative, with 1, not necessarily commutative) such that for every element a in R there exists an x in R with a = axa. One may think of x as a "weak inverse" of the element a; in general x is not uniquely determined by a. Von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left R-module is flat.
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In mathematics, a von Neumann ...... lement x in such that a = axa.
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Pierścień regularny w sensie v ...... u istnieje element spełniający
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数学において、フォン・ノイマン正則環（英: von Neum ...... xa となるとき（フォン・ノイマン）正則イデアルと呼ばれる。
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950,528,077
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author
L.A. Skornyakov
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id
R/r080830
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title
Regular ring
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subject
comment
In mathematics, a von Neumann ...... t every left R-module is flat.
@en
Pierścień regularny w sensie v ...... u istnieje element spełniający
@pl
数学において、フォン・ノイマン正則環（英: von Neum ...... xa となるとき（フォン・ノイマン）正則イデアルと呼ばれる。
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label
Pierścień regularny w sensie von Neumanna
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Von Neumann regular ring
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フォン・ノイマン正則環
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절대평탄환
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