List questions from polynomial-rings

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For what $k$ is $g_k\circ f_k$ invertible?

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Prove that the field $k(x)$ of rational functions over $k$ in the variable $x$ is not a finitely generated $k$-algebra.

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The 1-affine space is not isomorphic to the 1-affine space minus one point

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What are the coefficients of $x^2+2\in(\mathbb{Z}/\mathbb{Z}4)[x]?$

Published on 23 Mar 2026 - 1:55

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Prove that $\mathbb{Z}_{5}[x]/(x^2+1)$ is isomorphic to $\mathbb{Z}_{5} \times \mathbb{Z}_{5}$.

Published on 23 Mar 2026 - 7:01

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Polynomial ring over finite field - inverting a polynomial non-prime

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Descending Chain Condition

Published on 22 Mar 2026 - 17:00

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notation in congruence relation

Published on 22 Mar 2026 - 14:37

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Is the cardinality of the polynomial quotient ring $\mathbb{Z}_n [x] /f(x)$ always finite?

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Counting irreducible polynomials over finite fields

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Krull-Dimension of $k[X, Y , Z]/(Y-Z^2, XZ-Y^2)$

Published on 21 Mar 2026 - 1:46

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Noether polynomial ring over $2\Bbb Z$

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Find all irreducible polynomials of degrees $2$ and $3$ in $\Bbb{Z}_{2}[x]$.

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Finding all the ideals of $\mathbb{Z} [x]/(2, (x^3+1))$?

Published on 25 Mar 2026 - 3:07

List Question

Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.

For what $k$ is $g_k\circ f_k$ invertible?

Prove that the field $k(x)$ of rational functions over $k$ in the variable $x$ is not a finitely generated $k$-algebra.

The 1-affine space is not isomorphic to the 1-affine space minus one point

What are the coefficients of $x^2+2\in(\mathbb{Z}/\mathbb{Z}4)[x]?$

Prove that $\mathbb{Z}_{5}[x]/(x^2+1)$ is isomorphic to $\mathbb{Z}_{5} \times \mathbb{Z}_{5}$.

Polynomial ring over finite field - inverting a polynomial non-prime

Descending Chain Condition

notation in congruence relation

Is the cardinality of the polynomial quotient ring $\mathbb{Z}_n [x] /f(x)$ always finite?

Counting irreducible polynomials over finite fields

Krull-Dimension of $k[X, Y , Z]/(Y-Z^2, XZ-Y^2)$

Noether polynomial ring over $2\Bbb Z$

Find all irreducible polynomials of degrees $2$ and $3$ in $\Bbb{Z}_{2}[x]$.

Finding all the ideals of $\mathbb{Z} [x]/(2, (x^3+1))$?

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