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An ideal of a Noetherian ring with one associated prime

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#commutative-algebra #noetherian
330
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Proving Ascending Ideals Stabilize in PID

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#abstract-algebra #proof-explanation #ideals #principal-ideal-domains #noetherian
109
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Artin-Rees property in commutative Noetherian rings with unit

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#ring-theory #commutative-algebra #noetherian #primary-decomposition
106
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Proof Checking: Elements of Noetherian Domains may be factored into irreducibles

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#abstract-algebra #proof-verification #ring-theory #ideals #noetherian
202
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Example of a Noetherian domain which is not equidimensional

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#commutative-algebra #noetherian #integral-domain
277
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How could I construct a module $M$ that has exactly $n$ composition series?

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#abstract-algebra #ring-theory #modules #noetherian #artinian
253
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A completely reducible module is Artinian if and only if it is Noetherian.

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#abstract-algebra #modules #noetherian #artinian
100
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Noetherian domain whose fraction field is such that some specific proper submodules are projective

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#commutative-algebra #modules #noetherian #projective-module #integral-extensions
253
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If the completion of a module is trivial, must the module be trivial?

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#commutative-algebra #modules #noetherian
81
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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
410
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Unique prime ideal factorization in noetherian domains?

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#commutative-algebra #maximal-and-prime-ideals #noetherian #integral-domain
910
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$R$ noetherian, then every finitely generated $R$-module A has a resolution

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#abstract-algebra #commutative-algebra #noetherian
58
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Commutative Noetherian ring with distinct ideals having distinct index

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#ring-theory #commutative-algebra #cardinals #noetherian
210
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Are unique prime ideal factorization domains noetherian?

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#commutative-algebra #maximal-and-prime-ideals #noetherian #integral-domain
84
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Are unique prime ideal factorization domains locally noetherian?

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#commutative-algebra #maximal-and-prime-ideals #noetherian #integral-domain

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