query: If the matrix rings are isomorphic, then the scalars rings are isomorphic
positive_passages.docid: 153574
positive_passages.text: Uniqueness of Artin-Wedderburn decomposition
negative_passages.docid: 146715
negative_passages.text: A square matrix has the same minimal polynomial over its base field as it has over an extension field
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
negative_passages.docid: 6101
negative_passages.text: Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
negative_passages.docid: 55148
negative_passages.text: Why is this isomorphism $M \otimes_K L \stackrel{\simeq}{\longrightarrow} M^{[L:K]}$ an isomorphism of $M$ - algebras?
negative_passages.docid: 118781
negative_passages.text: product of ideals in matrix ring
negative_passages.docid: 60760
negative_passages.text: Ring homomorphism and characteristic
negative_passages.docid: 44923
negative_passages.text: Show that matrix under addition is isomorphic with the group of complex numbers under addition
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 26110
negative_passages.text: Canonical isomorphism between $\mathfrak{so}(3)$ and $\mathbb R^3$ with vector cross product
negative_passages.docid: 154581
negative_passages.text: Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$
negative_passages.docid: 74441
negative_passages.text: Zero divisors in matrix rings
negative_passages.docid: 136389
negative_passages.text: Finding an isomorphic subring of matrices
negative_passages.docid: 62711
negative_passages.text: Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 47086
negative_passages.text: Quotient rings and free modules