List questions from ring-theory

Published on 13 Apr 2026 - 3:05

927

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Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Published on 15 Apr 2026 - 4:31

166

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Number of Ring homomorphisms $\phi:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$

Published on 14 Apr 2026 - 18:44

54

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Finite fields isomorphisms and ideals

Published on 14 Apr 2026 - 13:50

134

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Quotient of the ring of Laurent polynomials

Published on 13 Apr 2026 - 10:46

85

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Show that if $S$ is a PID and $t\in S$ irreducible then $S/(t)$ is a field

Published on 15 Apr 2026 - 19:27

501

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If $\mathbb Q \otimes_\mathbb Z \mathbb Q \cong \mathbb Q^\mathbb N$, why is $\mathbb Q \otimes_\mathbb Z \mathbb Q$ a $1$-dim $\mathbb Q$-v.s.

Published on 16 Apr 2026 - 9:55

259

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Show that the McNuggets ring $A=\mathbb C[z^6,z^9,z^{20}]$ is not a UFD

Published on 12 Apr 2026 - 14:39

32

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Which one is correct definition of subring?

Published on 11 Apr 2026 - 9:14

92

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Is integral extension of noetherian ring noetherian?

Published on 12 Apr 2026 - 0:50

28

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natural localisation is bijective

Published on 27 Mar 2026 - 22:19

60

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Localization of Dedekind Domains

Published on 15 May 2026 - 0:12

1k

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Polynomial ring is not a UFD

Published on 14 Apr 2026 - 8:44

66

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The Fields of Fractions Induced by Two Similar, but Distinct Integral Domains

Published on 29 Apr 2026 - 16:17

168

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All ideals of $\mathbb{F}[x]/(f(x))$ in terms of factorization of $f(x)$

Published on 14 Apr 2026 - 13:29

List Question

Prime ideals of $\mathbb{Z}_p[X]$

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Number of Ring homomorphisms $\phi:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$

Finite fields isomorphisms and ideals

Quotient of the ring of Laurent polynomials

Show that if $S$ is a PID and $t\in S$ irreducible then $S/(t)$ is a field

If $\mathbb Q \otimes_\mathbb Z \mathbb Q \cong \mathbb Q^\mathbb N$, why is $\mathbb Q \otimes_\mathbb Z \mathbb Q$ a $1$-dim $\mathbb Q$-v.s.

Show that the McNuggets ring $A=\mathbb C[z^6,z^9,z^{20}]$ is not a UFD

Which one is correct definition of subring?

Is integral extension of noetherian ring noetherian?

natural localisation is bijective

Localization of Dedekind Domains

Polynomial ring is not a UFD

The Fields of Fractions Induced by Two Similar, but Distinct Integral Domains

All ideals of $\mathbb{F}[x]/(f(x))$ in terms of factorization of $f(x)$

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