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Are the rings $\mathbb{R}^2$ and $\mathbb{R}^3$ isomorphic?

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#abstract-algebra #ring-isomorphism
154
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What does $φ(a) = a$ mean in this statement?

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#abstract-algebra #polynomials #ring-theory #irreducible-polynomials #ring-isomorphism
60
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Showing that $(I+J)/(I\cap J)\cong (I+J)/I\times (I+J)/J$.

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#abstract-algebra #ring-theory #ring-isomorphism
324
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Isomorphisms for rings modulo ideals

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#abstract-algebra #ring-theory #ideals #ring-isomorphism
94
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What's the point of studying isomorphisms?

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#group-isomorphism #ring-isomorphism
678
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Proving 2 quotient rings are isomorphic

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#abstract-algebra #ring-theory #quotient-group #ring-isomorphism
112
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Need help to construct a ring isomorphism from $\mathbb{Z}_3[\sqrt2]$ $\rightarrow $ $\mathbb{Z}_3[i]$

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#abstract-algebra #ring-theory #ring-isomorphism
155
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Algebraic structure, division ring

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#abstract-algebra #vectors #ring-isomorphism #division-ring
829
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Isomorphisms of $\mathbb{R}[A]$ where $A$ is a $2\times2$ real matrix.

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#linear-algebra #matrices #ring-theory #minimal-polynomials #ring-isomorphism
139
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Prove or disprove ring $\mathbb{C}\times \mathbb{C}$ and ring Quaternion $H$ are isomorphic

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#quaternions #ring-isomorphism
114
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Product ring isomorphism from example 11.6.3 in Artin's Algebra

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#abstract-algebra #ring-theory #commutative-algebra #finite-fields #ring-isomorphism
276
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Showing that $\frac{\mathbb{R}[x]}{\langle x \rangle}$ and $\frac{\mathbb{R}[x]}{\langle x-1 \rangle}$ are not isomorphic as $\mathbb{R}[x]$ modules.

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#abstract-algebra #ring-theory #modules #ring-isomorphism #module-isomorphism
265
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Finding an isomorphic subring of matrices

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#abstract-algebra #ring-theory #group-isomorphism #ring-homomorphism #ring-isomorphism
114
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Abstract Algebra: Quotient ring, ideal, and isomorphism

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#abstract-algebra #ideals #ring-isomorphism
113
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Is the following ring isomorphism true?

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#ring-theory #intuition #ring-isomorphism

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