List questions from commutative-algebra

Published on 05 May 2026 - 5:45

173

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Does every valuation ring arise out of a valuation?

Published on 29 Apr 2026 - 12:57

529

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Noetherian local domain of dimension one

Published on 29 Apr 2026 - 12:43

1.1k

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Polynomial rings are regular

Published on 29 Apr 2026 - 12:42

310

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Dimension of Quotient of Noetherian local ring

Published on 29 Apr 2026 - 12:42

77

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localization of quotient of a polynomial ring

Published on 14 Apr 2026 - 6:56

238

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Calculating the residue field of $\mathbb{F}_q(t)$ with respect to the valuation $-\deg$

Published on 29 Apr 2026 - 12:57

289

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Hensel Lemma and cyclotomic polynomial

Published on 29 Apr 2026 - 12:41

109

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Spectrum of $\mathbb{Z}[\frac{1}{6}]$

Published on 29 Apr 2026 - 12:24

50

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In $A=k[[X^2,X^3]]$ no prime power is equal to $(X^3)$

Published on 18 Apr 2026 - 1:41

78

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Coordinate ring of $V \subset \mathbb{A}^n$ variety

Published on 10 May 2026 - 8:48

88

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Principal ideal over a ring

Published on 14 Apr 2026 - 0:17

74

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Integral Elements of $\mathbb{Q[x]}$ in $\mathbb{Q(x)}$

Published on 16 Apr 2026 - 22:22

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Let $K = \mathbb{Q}\left(\frac{-1+\sqrt{-3}}{2}\right)$. Show that $\mathcal{O}_K = \mathbb{Z}\left[\frac{-1+\sqrt{-3}}{2}\right]$.

Published on 17 Apr 2026 - 14:20

155

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injective hull of a ring that is not integral domain

Published on 07 May 2026 - 6:51

List Question

Krull dimension of a direct product of rings

Does every valuation ring arise out of a valuation?

Noetherian local domain of dimension one

Polynomial rings are regular

Dimension of Quotient of Noetherian local ring

localization of quotient of a polynomial ring

Calculating the residue field of $\mathbb{F}_q(t)$ with respect to the valuation $-\deg$

Hensel Lemma and cyclotomic polynomial

Spectrum of $\mathbb{Z}[\frac{1}{6}]$

In $A=k[[X^2,X^3]]$ no prime power is equal to $(X^3)$

Coordinate ring of $V \subset \mathbb{A}^n$ variety

Principal ideal over a ring

Integral Elements of $\mathbb{Q[x]}$ in $\mathbb{Q(x)}$

Let $K = \mathbb{Q}\left(\frac{-1+\sqrt{-3}}{2}\right)$. Show that $\mathcal{O}_K = \mathbb{Z}\left[\frac{-1+\sqrt{-3}}{2}\right]$.

injective hull of a ring that is not integral domain

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