List questions from integral-domain

Published on 22 Mar 2026 - 10:47

74

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Can we have $A \cong \mathrm{Frac}(A)[X]$?

Published on 22 Mar 2026 - 18:29

185

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Example for being an integral domain is not a local property.

Published on 25 Jun 2018 - 17:47

46

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Integral domain $0$ element

Published on 21 Mar 2026 - 23:32

409

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show the ring is an integral domain

Published on 22 Mar 2026 - 5:19

285

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If D is integral domain, then $b_m$ is unit

Published on 19 Jul 2018 - 21:07

706

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$(x)$ prime ideal in $R[x]$ iff $R$ integral domain by contrapositive

Published on 02 Aug 2018 - 18:26

70

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Extending a ring hom from $R \to L$ to $K \to L$, where $K$ is fraction field of domain $R$.

Published on 05 Aug 2018 - 22:57

165

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Are there any non-orientable integral domains?

Published on 22 Mar 2026 - 18:22

45

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if $p = charD \ \ $ then $ px = 0 \ \ \ \forall x \in D $.

Published on 22 Mar 2026 - 19:53

39

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If $b$ is not a prime in $R_1$ then is $R_2$ an integral domain or a field?

Published on 13 Sep 2018 - 8:11

152

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Irreducible Polynomial definition

Published on 22 Mar 2026 - 7:43

64

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Prove for every $i∈\Bbb Z∪{0}$ that $N(b^i)<N(b^{i+1})$ .

Published on 02 Nov 2018 - 16:26

1k

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Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.

Published on 04 Nov 2018 - 1:45

91

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When $\mathbb{Q}[\sqrt{n}i]$ and $\mathbb{Z}[\sqrt{n}i]$ normal?

Published on 07 Nov 2018 - 11:39

List Question

Why the integers form an integral domain?

Can we have $A \cong \mathrm{Frac}(A)[X]$?

Example for being an integral domain is not a local property.

Integral domain $0$ element

show the ring is an integral domain

If D is integral domain, then $b_m$ is unit

$(x)$ prime ideal in $R[x]$ iff $R$ integral domain by contrapositive

Extending a ring hom from $R \to L$ to $K \to L$, where $K$ is fraction field of domain $R$.

Are there any non-orientable integral domains?

if $p = charD \ \ $ then $ px = 0 \ \ \ \forall x \in D $.

If $b$ is not a prime in $R_1$ then is $R_2$ an integral domain or a field?

Irreducible Polynomial definition

Prove for every $i∈\Bbb Z∪{0}$ that $N(b^i)<N(b^{i+1})$ .

Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.

When $\mathbb{Q}[\sqrt{n}i]$ and $\mathbb{Z}[\sqrt{n}i]$ normal?

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