List questions from ring-theory

Published on 13 Jun 2018 - 2:17

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What is ℤ2[x]/I?

Published on 13 Jun 2018 - 2:49

1.1k

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Why the integers form an integral domain?

Published on 25 Mar 2026 - 3:07

39

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How two different elements belong to a polynomial implies the polynomial is a proper ideal?

Published on 28 Mar 2026 - 20:54

52

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How do I find a ring with a primary ideal having n elements?

Published on 22 Mar 2026 - 16:56

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The field of quotients of integral domain and two related questions

Published on 13 Jun 2018 - 21:43

175

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Index of Principal Ideal in a Subring of $\mathbb{Q}(\sqrt{-3})$

Published on 14 Jun 2018 - 2:10

210

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Completion and endomorphism ring of injective envelope

Published on 22 Mar 2026 - 12:43

37

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Do generating sets of ideals increase if ideals increase?

Published on 28 Mar 2026 - 20:52

68

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Show that $M_{n}(R)/M_{n}(I)\cong M_{n}(R/I)$

Published on 29 Mar 2026 - 4:41

736

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Why $0$ must be in the kernel of a ring?

Published on 15 Jun 2018 - 3:18

802

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Why proper ideal doesn't contain $1$?

Published on 15 Jun 2018 - 4:54

103

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How can I understand the First Isomorphism Theorem better?

Published on 15 Jun 2018 - 7:50

27

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Let $I$ be an ideal of $R$, if $m(x)$ is a polynomial of $I$ with the smallest degree, how can we prove $(m(x))\subset I$?

Published on 15 Jun 2018 - 8:21

164

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Prove/disprove: If $R'$ is a subring of $R$ and $R'$ is a domain, then $R$ is a domain.

Published on 15 Jun 2018 - 15:32

List Question

What does $\mathbb Z_2[x]$ means?

What is ℤ2[x]/I?

Why the integers form an integral domain?

How two different elements belong to a polynomial implies the polynomial is a proper ideal?

How do I find a ring with a primary ideal having n elements?

The field of quotients of integral domain and two related questions

Index of Principal Ideal in a Subring of $\mathbb{Q}(\sqrt{-3})$

Completion and endomorphism ring of injective envelope

Do generating sets of ideals increase if ideals increase?

Show that $M_{n}(R)/M_{n}(I)\cong M_{n}(R/I)$

Why $0$ must be in the kernel of a ring?

Why proper ideal doesn't contain $1$?

How can I understand the First Isomorphism Theorem better?

Let $I$ be an ideal of $R$, if $m(x)$ is a polynomial of $I$ with the smallest degree, how can we prove $(m(x))\subset I$?

Prove/disprove: If $R'$ is a subring of $R$ and $R'$ is a domain, then $R$ is a domain.

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