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15
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Ring isomorphism between $(k[x,y]/(xy))/(x+y-a)$ and $k\times k$

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#abstract-algebra #ring-theory #chinese-remainder-theorem #polynomial-rings #ring-isomorphism
81
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Showing that End$_{FG}V$ is isomorphic to $F$ as a ring.

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#ring-theory #field-theory #modules #ring-isomorphism #division-ring
115
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The ring $\frac{\mathbb{Z}[x]}{\langle x^n \rangle}$ is isomorphic to?

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#abstract-algebra #ring-theory #ideals #ring-homomorphism #ring-isomorphism
60
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Are two matrices isomorphic? (as rings and as group)

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#abstract-algebra #matrices #group-isomorphism #ring-isomorphism
113
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What is the example of non canonical isom?

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#abstract-algebra #group-isomorphism #ring-isomorphism
34
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Are field isomorphisms necessarily linear isomorphisms?

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#extension-field #vector-space-isomorphism #ring-isomorphism
61
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Isomorphism between $\mathbb{Z}[C_n]$ and $\mathbb{Z}[X]/(X^n-1)$

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#abstract-algebra #group-rings #ring-isomorphism
56
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If ring endomorphisms of finite dimensional vector spaces are isomorphic => Vector spaces and division rings are isomorphic

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#modules #vector-space-isomorphism #ring-isomorphism
27
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Necessity of irreducibility of polynomial over field

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#abstract-algebra #ring-theory #field-theory #irreducible-polynomials #ring-isomorphism
53
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Show $\mathbb{C}[x]/(x-i) \cong \mathbb{C}$ and $\mathbb{C}[x]/(x+i) \cong \mathbb{C}$

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#abstract-algebra #ring-theory #solution-verification #ring-isomorphism
62
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Missing a detail about Chinese Remainder Theorem and $Z$ Ring isomorphisms.

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#linear-algebra #ring-theory #modular-arithmetic #chinese-remainder-theorem #ring-isomorphism
55
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How to relate $\mathbb{Q}$ with $\mathbb{Z}$ using isomorphisms

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#abstract-algebra #ring-theory #ring-isomorphism
46
Views

Group algebra, cyclic group, ring isomorphism

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#ring-isomorphism #irreducible-representation
270
Views

Isomorphism between two quotient ring

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#abstract-algebra #ring-theory #ring-homomorphism #polynomial-rings #ring-isomorphism
39
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Consider the polynomial transform $p \mapsto \sum_{i=0}^{m-1} p(i) x^i \mod m$ - Prove the transformation is an isomorphism iff $m$ is prime.

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#linear-algebra #polynomials #modular-arithmetic #linear-transformations #ring-isomorphism

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