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Equivalent definitions of fractional ideals

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#commutative-algebra #ideals
115
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Graded ring, and its homogeneous ideals : $ I = \displaystyle \bigoplus_ {n \in \mathbb {Z}} (I \bigcap B_n) $

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#ring-theory #commutative-algebra
118
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On a localized ring tensor with a module

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#commutative-algebra
126
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A question regarding Hilbert's Nullstellensatz.

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#algebraic-geometry #commutative-algebra
514
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Weak nullstellansatz in Atiyah-Macdonald 5.17

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#algebraic-geometry #commutative-algebra
118
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Krull dimension of a direct limit of commutative rings

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#commutative-algebra #krull-dimension
2.4k
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Atiyah-Macdonald Exercise 2.15

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#abstract-algebra #commutative-algebra
76
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Questions regarding a proof of Nakayama's lemma.

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#commutative-algebra
3.7k
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How to show that $\Bbb Z[x,y,z,w]/(xw-zy)$ is not a UFD

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#abstract-algebra #ring-theory #commutative-algebra #unique-factorization-domains
128
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$\operatorname{supp}(M) \subseteq \operatorname{supp}(N) \iff f_I(M)\subseteq f_I(N) $?

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#commutative-algebra #modules #local-cohomology
955
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The ring $R$ is a field iff $R$ has a finitely generated divisible module

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#ring-theory #commutative-algebra #modules #finitely-generated
1.4k
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Universal property of polynomial ring in $\mathbf{CRING}$

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#abstract-algebra #commutative-algebra #category-theory
905
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Does it hold that the $p$-adic completion of the integers equals the completion of the localization in $p$?

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#number-theory #commutative-algebra #algebraic-number-theory
665
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A finite commutative ring with 1 whose elements satisfy a particular equation

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#abstract-algebra #ring-theory #commutative-algebra #field-theory
2.2k
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Is $\mathbb{C}[x,y] / (y^2-x^3)$ a PID?

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#abstract-algebra #ring-theory #commutative-algebra #principal-ideal-domains

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