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Equivalence of definitions of Krull dimension of a module

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#commutative-algebra #modules #krull-dimension #dimension-theory-algebra
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Why is every Noetherian zero-dimensional scheme finite discrete?

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#algebraic-geometry #schemes #krull-dimension
1.4k
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When is the generic point of an integral noetherian scheme open (reference)?

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#reference-request #algebraic-geometry #commutative-algebra #krull-dimension
351
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What is the Krull dimension of this local ring

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#algebraic-geometry #commutative-algebra #ring-theory #krull-dimension
330
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Krull dimension of this local ring

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#abstract-algebra #polynomials #commutative-algebra #ring-theory #krull-dimension
202
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Krull dimension bound of a Fitting ideal

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#abstract-algebra #commutative-algebra #ideals #krull-dimension
617
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Krull dimension and graded prime ideals

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#commutative-algebra #ideals #graded-modules #krull-dimension #graded-rings
1.4k
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surjective map of rings with same dimension

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#commutative-algebra #krull-dimension
615
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Calculation of codimension

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#abstract-algebra #commutative-algebra #krull-dimension
2.7k
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Krull dimension of some quotient rings

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#commutative-algebra #krull-dimension
1.1k
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Krull dimension and localization of a module

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#commutative-algebra #modules #krull-dimension #noetherian
4k
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Krull dimension of quotient rings

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#commutative-algebra #proof-verification #krull-dimension
1.2k
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Dimension of quotient rings and zero divisors

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#commutative-algebra #krull-dimension
968
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Dimension of graded module

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#commutative-algebra #graded-modules #krull-dimension #noetherian
113
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Why does $\dim(A/P)\leq n$ imply $\dim(A)\leq n$ for an algebra $A$ over a field $K$ with $P\in \operatorname{Spec}(A)$.

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#commutative-algebra #krull-dimension

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