List questions from abstract-algebra

Published on 10 Apr 2026 - 17:03

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Give an example of a group $G$ with an injective homomorphism $G \to G$, which is not an isomorphism

Published on 29 Jan 2018 - 21:59

184

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Showing Element is Not part of Multiplicative group of Integers mod $n$

Published on 11 Apr 2026 - 3:27

62

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Complex integration and bilinear operators

Published on 12 Apr 2026 - 17:22

439

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Find the ideals of $S^{-1}R$

Published on 09 Apr 2026 - 0:31

1.1k

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Proof on order of element of cyclic group must divide the order of the group.

Published on 12 Apr 2026 - 21:00

388

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Mathematical phantoms

Published on 12 Apr 2026 - 0:11

55

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Isometries of non-singular bilinear space over field of characteristic $\neq 2$

Published on 28 Mar 2026 - 10:41

253

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$f(x) = x^6, g(x) = x^{10}$ endomorphisms $\implies G$ is abelian

Published on 24 Mar 2026 - 23:45

325

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Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Published on 25 Mar 2026 - 6:13

674

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Disjoint cycle decomposition in $A_n$

Published on 30 Jan 2018 - 13:40

555

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Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Published on 09 Apr 2026 - 0:28

110

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Irreducibility of $f(x)=x^4+4x-1$

Published on 09 Apr 2026 - 0:08

146

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Is there any intermediate fields between these two fields？

Published on 09 Apr 2026 - 1:07

137

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Consider polynomial $X^3-3X+1$ If $\alpha$ is a root $\alpha^3-3 \alpha+1=0 $

Published on 26 Mar 2026 - 12:35

List Question

Proof of isomorphism

Give an example of a group $G$ with an injective homomorphism $G \to G$, which is not an isomorphism

Showing Element is Not part of Multiplicative group of Integers mod $n$

Complex integration and bilinear operators

Find the ideals of $S^{-1}R$

Proof on order of element of cyclic group must divide the order of the group.

Mathematical phantoms

Isometries of non-singular bilinear space over field of characteristic $\neq 2$

$f(x) = x^6, g(x) = x^{10}$ endomorphisms $\implies G$ is abelian

Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Disjoint cycle decomposition in $A_n$

Find all surjective ring homomorphisms $\phi:\mathbb{R}[x] \rightarrow \mathbb{R}.$

Irreducibility of $f(x)=x^4+4x-1$

Is there any intermediate fields between these two fields？

Consider polynomial $X^3-3X+1$ If $\alpha$ is a root $\alpha^3-3 \alpha+1=0 $

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