List questions from abstract-algebra

Published on 15 Apr 2026 - 23:12

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Tower of integral extensions

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446

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Is this the (real) algebraic numbers?

Published on 10 Apr 2026 - 0:40

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Reference request for studying Ring of continious functions

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140

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Prove that $\mathbb{Q}^{*} \cong (\mathbb{Z}[x],+)$

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34

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The attributes of the defined direct product.

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Zeros of power series with polynomially bounded integer coefficients

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823

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Show that a complex polynomial has a root inside a disk

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104

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If $S<G:=\text{Gal}(E/R)$ is a Sylow 2-subgroup, then $[\text{Fix}_E(S):R] = [G:S]$

Published on 18 Apr 2026 - 8:29

55

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R is integral domain prove that

Published on 12 Apr 2026 - 13:25

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how to check whether it is a Galois extension.

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111

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What is the motivation of the identity $x\circ(a\circ b)=(((x\circ b)\circ a )\circ b$?

Published on 25 Apr 2026 - 14:47

34

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Number of polynomials in a finite commutative ring with n elements of degree d and of degree 2 in $R[x_1,x_2]$?

Published on 16 Apr 2026 - 11:37

23

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What is the ideal of the given ring?

Published on 11 Apr 2026 - 17:39

70

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Which of these principle ideals is maximal in $\mathbb{Z}[x]$?

Published on 16 Apr 2026 - 21:29

List Question

Polynomial ring as a finite algebra over a subring

Tower of integral extensions

Is this the (real) algebraic numbers?

Reference request for studying Ring of continious functions

Prove that $\mathbb{Q}^{*} \cong (\mathbb{Z}[x],+)$

The attributes of the defined direct product.

Zeros of power series with polynomially bounded integer coefficients

Show that a complex polynomial has a root inside a disk

If $S<G:=\text{Gal}(E/R)$ is a Sylow 2-subgroup, then $[\text{Fix}_E(S):R] = [G:S]$

R is integral domain prove that

how to check whether it is a Galois extension.

What is the motivation of the identity $x\circ(a\circ b)=(((x\circ b)\circ a )\circ b$?

Number of polynomials in a finite commutative ring with n elements of degree d and of degree 2 in $R[x_1,x_2]$?

What is the ideal of the given ring?

Which of these principle ideals is maximal in $\mathbb{Z}[x]$?

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