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Is the ring $A[x_1, \ldots, x_n]$ Cohen-Macaulay? Does the dimension formula hold?

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#commutative-algebra #maximal-and-prime-ideals #krull-dimension #cohen-macaulay
319
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When will $A[x_1, \ldots, x_n]$ satisfy the dimension formula?

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#commutative-algebra #maximal-and-prime-ideals #krull-dimension
304
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Prove that an ideal $ \mathfrak{m} $ of a commutative ring $ R $ is maximal iff $ R/\mathfrak{m} $ is simple.

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#abstract-algebra #ring-theory #commutative-algebra #ideals #maximal-and-prime-ideals
290
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$R\subset S$ rings conditions implying that there are at most $t$ maximal ideals in $S$ lying over any maximal ideal in $R$

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#commutative-algebra #maximal-and-prime-ideals
227
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Maximal ideals of R[x]/(f(x))

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#ring-theory #quotient-spaces #maximal-and-prime-ideals
5.8k
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Maximal Ideals of $\mathbb C[x, y]$

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra #maximal-and-prime-ideals
1.6k
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For $I,J$ ideals $P$ Prime ideal, show that $IJ\subset P \iff I\cap J \subset P$

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#ring-theory #ideals #maximal-and-prime-ideals
1.8k
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Dimension of a quotient ring

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#commutative-algebra #maximal-and-prime-ideals #krull-dimension
76
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Which primes belong to the support of $S^{-1}M$ with respect to $R$

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#abstract-algebra #ring-theory #commutative-algebra #modules #maximal-and-prime-ideals
2.5k
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About Relatively Prime Ideals

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
35
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A question on $R$-modules

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#ring-theory #modules #ideals #maximal-and-prime-ideals
300
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Prime ideals and maximal ideals

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#abstract-algebra #maximal-and-prime-ideals
688
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How to show that an ideal is maximal

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
215
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Maximal ideal of polynomial ring over a subfield

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#abstract-algebra #commutative-algebra #ideals #maximal-and-prime-ideals
3.1k
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Every prime ideal is maximal

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals

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