List questions from ring-isomorphism

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matrix first isomorphism problem

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Finding a homomorphism from a polynomial to matrix

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List Question

the ring $\frac{A[X]}{(X-a_{1},...,X-a_{n})}$ is isomorphic to A

matrix first isomorphism problem

Ring Isomomorphism?

Showing that if $ker(\theta) \subseteq A$ (an ideal in R) then $R/A \simeq S/\theta(A)$

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

Showing a ring homomorphism is an isomorphism

Third Isomorphism Theorem for Rings confusions

Isomorphism from $R[x,y] / (x, y - x^2)$ to $R$

How to determine if there exists an isomorphism to a subring of $\mathbb{R}$ from a ring and ideal.

Isomorphism of rings between 2 non fields

Substitution on $\mathbb{R}$ as isomorphisms

For ring homomorphism $\phi:R\to S$, prove that $\phi$ is an isomorphism iff $\phi$ is onto and $ker(\phi)=\left \{0_{R} \right \}$.

Show that the ring isomorphism $\phi :R[x]\to S[x]$ is well-defined.

$ R \cong R s $ as rings if and only if $ s $ is invertible

Finding a homomorphism from a polynomial to matrix

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