List questions from ring-theory

Published on 28 Mar 2026 - 8:32

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About the definition of an integral element in commutative rings

Published on 23 Feb 2026 - 2:29

59

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$\ {-}4\equiv 1\pmod{\!5}\ $ so $\ x^2+1 = (x-2)(x+2)\ $ in $\Bbb Z_5[x]$

Published on 01 Sep 2018 - 14:47

166

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Are there any non-orientable integral domains?

Published on 25 Mar 2026 - 3:00

568

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If $S$ is a Noetherian ring and $R\subset S$ is a sub-ring, prove that $R$ is Noetherian or a counterexample

Published on 25 Mar 2026 - 11:13

51

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Proof Verification: Show that $R = I + J$, where $R$ is a PID and $I,J$ are ideals

Published on 02 Sep 2018 - 4:28

166

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Algorithm to find relations between polynomials

Published on 25 Mar 2026 - 7:38

348

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To prove the Second Isomorphism Theorem for modules from the opposite direction:

Published on 28 Mar 2026 - 12:48

39

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What is this module endomorphism for a given algebra?

Published on 24 Mar 2026 - 23:42

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Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

Published on 28 Mar 2026 - 8:34

50

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Explanation for the definition of an Ideal

Published on 27 Mar 2026 - 10:11

31

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(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

Published on 26 Mar 2026 - 2:47

309

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Action by automorphism group of a ring $R$ on $\mathrm{Spec}(R)$

Published on 25 Mar 2026 - 11:20

77

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Proving that $\mathbb{Q}[X] = (X-1) + (X+1)$

Published on 29 Mar 2026 - 10:14

31

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Question regarding the definition of principal ideal

Published on 27 Mar 2026 - 10:09

List Question

Theorem 10.2 in Matsumura's commutative ring theory

About the definition of an integral element in commutative rings

$\ {-}4\equiv 1\pmod{\!5}\ $ so $\ x^2+1 = (x-2)(x+2)\ $ in $\Bbb Z_5[x]$

Are there any non-orientable integral domains?

If $S$ is a Noetherian ring and $R\subset S$ is a sub-ring, prove that $R$ is Noetherian or a counterexample

Proof Verification: Show that $R = I + J$, where $R$ is a PID and $I,J$ are ideals

Algorithm to find relations between polynomials

To prove the Second Isomorphism Theorem for modules from the opposite direction:

What is this module endomorphism for a given algebra?

Every maximal ideal of a commutative unitary ring is prime (Proof explanation)

Explanation for the definition of an Ideal

(Proof explanation) In integral domain let there be a prime ideal $(a)$ then $a$ is irreducible.

Action by automorphism group of a ring $R$ on $\mathrm{Spec}(R)$

Proving that $\mathbb{Q}[X] = (X-1) + (X+1)$

Question regarding the definition of principal ideal

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