List questions from integral-domain

Published on 14 Apr 2026 - 1:54

77

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

Published on 10 Apr 2026 - 20:39

190

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

Published on 22 Apr 2026 - 4:30

50

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Integral domain $0$ element

Published on 12 Apr 2026 - 21:01

413

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show the ring is an integral domain

Published on 11 Apr 2026 - 13:27

287

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

Published on 14 Apr 2026 - 5:10

709

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

Published on 16 Apr 2026 - 13:39

73

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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 10 Apr 2026 - 12:32

168

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Are there any non-orientable integral domains?

Published on 15 Apr 2026 - 13:03

47

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

Published on 14 Apr 2026 - 21:32

44

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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 17 Apr 2026 - 1:03

155

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Irreducible Polynomial definition

Published on 10 Apr 2026 - 20:18

67

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

Published on 15 Apr 2026 - 18:55

1.1k

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

Published on 14 Apr 2026 - 2:45

97

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

Published on 29 Apr 2026 - 12:57

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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