24 Isomorphic groups but not isomorphic rings 8 Prove that $\varphi(2n)=2\varphi(n)$ if $n$ is even. 8 Fundamental Isomorphism Theorem 8 Simple linear algebra problem: prove a matrix is invertible 7 Showing automorphism group is trivial

### Reputation (7,043)

 +10 Significance of unity in ring for isomorphism +25 Multiplicative map giving the roots of $f (x_1 , . . . , x_n ) ∈ \Bbb Z[x_1 , . . . , x_n ]$ +35 Prove that $R/I$ and $S/\phi(I)$ are isomorphic +15 Determine which $p \in (0,\infty)$ where $f \in \mathcal{L}^p(\lambda)$.

### Questions (75)

 14 No bounded surjective linear map $L^{\infty} \to L^1$ 8 Jordan-Chevalley vs Jordan normal decomposition 6 Strange contour integral 5 $\textrm{Re}(f'(z)) > 0$ but $f$ is not injective. 5 Linear algebra problem from dummite & foote

### Tags (166)

 140 abstract-algebra × 70 39 polynomials × 15 57 real-analysis × 60 34 linear-algebra × 17 55 ring-theory × 16 32 group-theory × 22 52 calculus × 30 32 limits × 16 43 field-theory × 24 28 complex-analysis × 33

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