List questions from integral-domain

Published on 10 Sep 2021 - 1:16

182

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If $\gcd(a,b)\sim 1$, $\gcd(a,c)\sim1$, then $\gcd(a,bc)\sim1$?

Published on 24 Feb 2026 - 0:48

96

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Show that $U(R)$ has at most $n$ elements of order $n$, for every positive integer $n$

Published on 16 Sep 2021 - 19:25

39

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Doubt in proof that given a commutative ring $(I_p, +, \cdot)$ is a field iff p is prime

Published on 27 Oct 2021 - 9:36

190

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Why are some $\Bbb Q[\sqrt n]$ not UFDs when they are fields, so UFDs?

Published on 01 Nov 2021 - 21:11

1.4k

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Show that no ring of order 6 is an integral domain.

Published on 24 Feb 2026 - 1:59

55

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Show that $\mathbb{Q}[x,y]/I$ is a domain

Published on 06 Nov 2021 - 10:38

984

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Prove that the Gaussian integers Z [i] form an integral domain

Published on 26 Mar 2026 - 19:19

127

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Idempotent elements of a quotient ring.

Published on 17 Nov 2021 - 11:42

35

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Arithmetic structure including both unique factorization and Dedekind domains

Published on 27 Mar 2026 - 15:05

85

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Is it really necessary to work with the fraction field here?

Published on 26 Nov 2021 - 23:10

160

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Proof that gaussian integers are an integral domain by contradiction.

Published on 26 Mar 2026 - 19:18

59

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Equality of principal domains $(a) = (b)$ does not imply that $a = bu$ for some unit $u$.

Published on 29 Nov 2021 - 5:52

198

Views

Are Boolean rings integral domains?

Published on 23 Feb 2026 - 4:44

55

Views

If $D$ is an integral domain which is not a field, then $D[\alpha]$ is not a field.

Published on 10 Dec 2021 - 0:34

List Question

Subring of a commutative ring with unity implies ring is an integral domain

If $\gcd(a,b)\sim 1$, $\gcd(a,c)\sim1$, then $\gcd(a,bc)\sim1$?

Show that $U(R)$ has at most $n$ elements of order $n$, for every positive integer $n$

Doubt in proof that given a commutative ring $(I_p, +, \cdot)$ is a field iff p is prime

Why are some $\Bbb Q[\sqrt n]$ not UFDs when they are fields, so UFDs?

Show that no ring of order 6 is an integral domain.

Show that $\mathbb{Q}[x,y]/I$ is a domain

Prove that the Gaussian integers Z [i] form an integral domain

Idempotent elements of a quotient ring.

Arithmetic structure including both unique factorization and Dedekind domains

Is it really necessary to work with the fraction field here?

Proof that gaussian integers are an integral domain by contradiction.

Equality of principal domains $(a) = (b)$ does not imply that $a = bu$ for some unit $u$.

Are Boolean rings integral domains?

If $D$ is an integral domain which is not a field, then $D[\alpha]$ is not a field.

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