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- Krull_dimension abstract "In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.The Krull dimension has been introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal I in a polynomial ring R is the Krull dimension of R/I.A field k has Krull dimension 0; more generally, k[x1, ..., xn] has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.".
- Krull_dimension wikiPageID "56079".
- Krull_dimension wikiPageRevisionID "565374685".
- Krull_dimension hasPhotoCollection Krull_dimension.
- Krull_dimension subject Category:Commutative_algebra.
- Krull_dimension subject Category:Dimension.
- Krull_dimension comment "In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring.".
- Krull_dimension label "Dimension de Krull".
- Krull_dimension label "Dimensione di Krull".
- Krull_dimension label "Dimensión de Krull".
- Krull_dimension label "Krull dimension".
- Krull_dimension label "Krull-dimensie".
- Krull_dimension label "Krulldimension".
- Krull_dimension label "Размерность Крулля".
- Krull_dimension label "クルル次元".
- Krull_dimension label "克鲁尔维数".
- Krull_dimension sameAs Krulldimension.
- Krull_dimension sameAs Dimensión_de_Krull.
- Krull_dimension sameAs Dimension_de_Krull.
- Krull_dimension sameAs Dimensione_di_Krull.
- Krull_dimension sameAs クルル次元.
- Krull_dimension sameAs 크룰_차원.
- Krull_dimension sameAs Krull-dimensie.
- Krull_dimension sameAs m.0fjqz.
- Krull_dimension sameAs Q1225713.
- Krull_dimension sameAs Q1225713.
- Krull_dimension wasDerivedFrom Krull_dimension?oldid=565374685.
- Krull_dimension isPrimaryTopicOf Krull_dimension.