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Residue fields of $\mathbb Z[X_1,...,X_n]$ are always finite ?

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#polynomials #ring-theory #commutative-algebra #field-theory #maximal-and-prime-ideals
245
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Exercises for commutative algebra

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#commutative-algebra #soft-question #big-list
169
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Ideal of distinct points

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#algebraic-geometry #commutative-algebra #ideals
529
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Integral Closure Flat

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#ring-theory #commutative-algebra #flatness
202
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Product of gcd and lcm for multivariate polynomials

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#polynomials #commutative-algebra #gcd-and-lcm #least-common-multiple
78
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Filtration in crystalline Poincaré Lemma

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#algebraic-geometry #commutative-algebra #homological-algebra #filtrations
263
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Quotient of monomial ideals

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#polynomials #ring-theory #commutative-algebra #monomial-ideals
65
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Faithfully Flat imply $aA = aB \cap A$

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#commutative-algebra #flatness
253
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Noetherian Catenary ring and Cohen-Macaulay ring

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#abstract-algebra #commutative-algebra #cohen-macaulay
157
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Local properties concerning finitely generated modules over a noetherian ring

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#algebraic-geometry #commutative-algebra
69
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Viewing algebraic varieties as Homomorphism

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#algebraic-geometry #commutative-algebra
118
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Homogeneous prime ideals and grade zero elements

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#algebraic-geometry #commutative-algebra
79
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$\bigcap_{n\in\mathbb{N}} I^n = (0)$ if and only if no zero divisor of $R$ is of the form $1-z$ with $z\in I$.

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#abstract-algebra #ring-theory #commutative-algebra #ideals #noetherian
147
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Let $R \subseteq S$ be two local PIDs with the same field of fractions, then $R=S$.

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#abstract-algebra #ring-theory #commutative-algebra #localization
127
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On the number of multiplicative sub-monoids of integers mod $n$

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#abstract-algebra #elementary-number-theory #ring-theory #commutative-algebra

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