Question

ID's, PID's, Noetherian rings and valuation rings: implications amongst them

score 53 · Answer 1 · 2026-03-26 22:53:47

53

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ID's, PID's, Noetherian rings and valuation rings: implications amongst them

Published on 26 Mar 2026 - 22:53

score 38 · Answer 2 · 2024-02-02 22:51:54

38

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Algorithms to decompose a graded module over R[x], where R is a PID

Published on 02 Feb 2024 - 22:51

score 72 · Answer 3 · 2026-03-27 06:05:01

72

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Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Published on 27 Mar 2026 - 6:05

score 79 · Answer 4 · 2026-03-29 03:36:06

79

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Explicit proof of the fact that a non integrally closed domain is not a UFD

Published on 29 Mar 2026 - 3:36

score 78 · Answer 5 · 2026-03-29 03:36:42

78

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Need help understanding the proof that if $R$ is a PID, every nonzero, nonunit elements of $R$ is a product of irreducibles.

Published on 29 Mar 2026 - 3:36

score 68 · Answer 6 · 2026-03-29 04:26:31

68

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Need help understanding the proof showing the existence of gcd in an UFD.

Published on 29 Mar 2026 - 4:26

score 68 · Answer 7 · 2026-03-29 04:26:31

68

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Explicit proof of the fact that a domain which is not a UFD is not a PID

Published on 29 Mar 2026 - 4:26

score 83 · Answer 8 · 2024-02-19 22:59:38

83

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Where does $p^t$ come from in $R=\{\frac{a}{b}\in \mathbb{Q}\mid p\not\mid b, \text{ for some prime-}p \}$

Published on 19 Feb 2024 - 22:59

score 88 · Answer 9 · 2024-02-22 19:27:16

88

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If $I$ is an ideal of $R=\{\frac{a}{b}\in \mathbb{Q}\mid p\not\mid b\}$, for some fixed prime $p$, show that $(p^t)\subset I.$

Published on 22 Feb 2024 - 19:27

score 34 · Answer 10 · 2024-02-25 22:08:24

34

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Prove every ideal in ring of integers is principal

Published on 25 Feb 2024 - 22:08

score 33 · Answer 11 · 2024-03-02 17:21:44

33

Views

Determine the domain-sets of $f(z)=z\bar{z}/(z^2+\bar{z}^2)$

Published on 02 Mar 2024 - 17:21

score 18 · Answer 12 · 2024-03-02 18:05:43

18

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Determine the domain-sets of $ Log(e^z-e^{-z})$

Published on 02 Mar 2024 - 18:05

score 36 · Answer 13 · 2024-03-12 22:51:48

36

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The polynomial ideal associated to a prime ideal is prime

Published on 12 Mar 2024 - 22:51

score 14 · Answer 14 · 2026-03-28 04:09:10

14

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For a PID $R$ prove that restriction-of-scalars induces equivalence of categories $\coprod_p (R_{(p)}-\mathrm{mod})_{tors}\to (R-\mathrm{mod})_{tors}$

Published on 28 Mar 2026 - 4:09

score 47 · Answer 15 · 2026-03-27 10:24:20

47

Views

Under what conditions can Noetherian /artinian rings be considered principal ideal domain.

Published on 27 Mar 2026 - 10:24

List Question

ID's, PID's, Noetherian rings and valuation rings: implications amongst them

Algorithms to decompose a graded module over R[x], where R is a PID

Let $R$ be a P.I.D. and let $a \neq 0$ be an element in $R$. Prove that for a prime element $p$, $p(R/(a)) = ((p) + (a))/(a)$.

Explicit proof of the fact that a non integrally closed domain is not a UFD

Need help understanding the proof that if $R$ is a PID, every nonzero, nonunit elements of $R$ is a product of irreducibles.

Need help understanding the proof showing the existence of gcd in an UFD.

Explicit proof of the fact that a domain which is not a UFD is not a PID

Where does $p^t$ come from in $R=\{\frac{a}{b}\in \mathbb{Q}\mid p\not\mid b, \text{ for some prime-}p \}$

If $I$ is an ideal of $R=\{\frac{a}{b}\in \mathbb{Q}\mid p\not\mid b\}$, for some fixed prime $p$, show that $(p^t)\subset I.$

Prove every ideal in ring of integers is principal

Determine the domain-sets of $f(z)=z\bar{z}/(z^2+\bar{z}^2)$

Determine the domain-sets of $ Log(e^z-e^{-z})$

The polynomial ideal associated to a prime ideal is prime

For a PID $R$ prove that restriction-of-scalars induces equivalence of categories $\coprod_p (R_{(p)}-\mathrm{mod})_{tors}\to (R-\mathrm{mod})_{tors}$

Under what conditions can Noetherian /artinian rings be considered principal ideal domain.

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