List questions from ring-theory

Published on 16 Apr 2026 - 3:37

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Let $R$ be the ring of continuous real-valued functions on the interval $(0, 1)$ and and prove that $I=\{f∈R:f (1/3)=0\}$ is a maximal ideal in $R$

Published on 16 Apr 2026 - 0:57

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Field homomorphism is onto

Published on 25 Mar 2026 - 19:01

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Let $\varphi\colon R\to(R/I)\oplus(R/J)$ where $\varphi(r) = (r + I, r + J)$. Show $\varphi$ is an isomorphism iff $I + J = R$ and $I \cap J = \{0\}$.

Published on 26 Mar 2026 - 8:02

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Confusion around definition of greatest common divisor

Published on 14 Apr 2026 - 10:10

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Units in $\Bbb Z / 3 \Bbb Z[x] / I$ where $I=(x^3+2x^2)$

Published on 16 Apr 2026 - 16:38

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Motivation for contractions/extensions of ideals

Published on 08 Apr 2026 - 20:48

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Proof in idealization of almost clean ring.

Published on 26 Mar 2026 - 4:16

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What are the zero divisors of the ring $\mathbb Z_n[i]$, where $n$ has only one prime factor which is congruent to 3 (mod 4)?

Published on 10 May 2026 - 16:13

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Is $\Bbb Z / n \Bbb Z$ a PID?

Published on 09 Apr 2026 - 18:23

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(Left) Noetherian domains and Torsion submodules

Published on 16 Apr 2026 - 20:33

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What does the notation $[R':x]_R$ mean in this context?

Published on 12 Apr 2026 - 21:30

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How to find the multiplicative inverse of $a+b\sqrt{2}$ in $\mathbb{Q}({\sqrt{2}})$

Published on 28 Apr 2026 - 20:14

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How to show that an abelian group is a right $R$-module?

Published on 13 Apr 2026 - 5:52

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primitive polynomial and irreducible

Published on 12 Apr 2026 - 22:16

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The number of units in the quotient ring $\Bbb Z_5[x]/(x^4-1)$

Let $R$ be the ring of continuous real-valued functions on the interval $(0, 1)$ and and prove that $I=\{f∈R:f (1/3)=0\}$ is a maximal ideal in $R$

Field homomorphism is onto

Let $\varphi\colon R\to(R/I)\oplus(R/J)$ where $\varphi(r) = (r + I, r + J)$. Show $\varphi$ is an isomorphism iff $I + J = R$ and $I \cap J = \{0\}$.

Confusion around definition of greatest common divisor

Units in $\Bbb Z / 3 \Bbb Z[x] / I$ where $I=(x^3+2x^2)$

Motivation for contractions/extensions of ideals

Proof in idealization of almost clean ring.

What are the zero divisors of the ring $\mathbb Z_n[i]$, where $n$ has only one prime factor which is congruent to 3 (mod 4)?

Is $\Bbb Z / n \Bbb Z$ a PID?

(Left) Noetherian domains and Torsion submodules

What does the notation $[R':x]_R$ mean in this context?

How to find the multiplicative inverse of $a+b\sqrt{2}$ in $\mathbb{Q}({\sqrt{2}})$

How to show that an abelian group is a right $R$-module?

primitive polynomial and irreducible

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