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R is a regular local ring of dimension $d$, and $I$ an ideal. If $R/I$ has depth $d − 1$, then $I$ is principal.

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#commutative-algebra
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Localization of a polynomial ring at a maximal ideal

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#algebraic-geometry #commutative-algebra
147
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Dimension of Kahler differentials of Laurent series over perfect field.

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#algebraic-geometry #commutative-algebra
354
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Is every minimal set of generators for a homogeneous ideal composed by homogeneous elements?

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#commutative-algebra #graded-rings
496
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Ring of regular functions on an open set of spectrum of $R$ is a subring of the field of fractions of $R$.

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#algebraic-geometry #commutative-algebra
261
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The Relationship Between Cohomological Dimension and Support

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#commutative-algebra #modules #homological-algebra #local-cohomology
680
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Krull dimension of a quotient ring

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#commutative-algebra #irreducible-polynomials #krull-dimension
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Is Frobenius the only magical automorphism?

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#commutative-algebra #galois-theory
359
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When is $N\otimes_A B \to N$ an isomorphism?

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#abstract-algebra #commutative-algebra #modules #tensor-products
2k
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Uniqueness of tensor product

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#abstract-algebra #commutative-algebra
949
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Number of generators in a tensor product

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#abstract-algebra #commutative-algebra #tensor-products
170
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A Question from Algebraic Geometry

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#algebraic-geometry #commutative-algebra
119
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Factorization of an ideal in a number field

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#abstract-algebra #number-theory #commutative-algebra
279
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Equivalent condition for Jacobson radical

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#abstract-algebra #ring-theory #commutative-algebra
69
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Parametric ideal decomposition

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#algebraic-geometry #commutative-algebra #complex-geometry #groebner-basis

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