### Answers (139)

 57 Two metrics induce the same topology, but one is complete and the other isn't 38 Idempotents in a local ring 27 Irreducibility of $f(x)=x^4+3x^3-9x^2+7x+27$ 27 How to understand compactness? 16 Is addition continuous?

### Reputation (7,430)

 +20 Idempotents in a local ring +10 Two metrics induce the same topology, but one is complete and the other isn't +10 a nonmeasurable set $E$ of finite measure and a $G_{\delta}$ set $G$ that contains $E$ +10 Why do elementary matrix operations not affect the row space of a given matrix?

### Questions (12)

 6 almost n-th power in a field 6 Can disjoint triangles be separated by one of the lines they define? 4 Galois action on central simple algebras 3 Norm-Euclidean fields 3 Discriminant of $\mathbb{Z}[a,b]$

### Tags (128)

 157 abstract-algebra × 46 57 complete-spaces 126 general-topology × 11 55 commutative-algebra × 6 80 ring-theory × 11 52 linear-algebra × 21 61 examples-counterexamples × 2 45 polynomials × 10 58 metric-spaces × 3 44 ideals × 3

### Bookmarks (12)

 26 Expressing a root of a polynomial as a rational function of another root 25 Is there a function with this property? 25 Prove that $\lfloor \sqrt{p} \rfloor + \lfloor \sqrt{2p} \rfloor +…+ \lfloor \sqrt{\frac{p-1}{4}p} \rfloor = \frac{p^2 - 1}{12}$ 12 Almost identical map 12 Two seemingly unrelated puzzles have very similar solutions; what's the connection?

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