### Questions (48)

 9 If $I^n = 0$ and $M$ is a simple module, then $IM = 0.$ 5 A group with an infinite cyclic normal subgroup that has a finite cyclic quotient is abelian 5 Is there a way to get all the permutation braids of a braid group? 5 Methods to show an ideal in the ring of integers $\mathcal{O}_K$ is a proper ideal 4 Find $\lim\limits_{t\to\infty}x(t)$ if $x'= (x-y)(1-x^2-y^2)$, $y' = (x+y)(1-x^2-y^2)$

### Reputation (1,036)

 +5 Image of dual map is annihilator of kernel +5 Limits in functor categories can be computed pointwise +20 Find $\lim\limits_{t\to\infty}x(t)$ if $x'= (x-y)(1-x^2-y^2)$, $y' = (x+y)(1-x^2-y^2)$ +5 Deciding whether the maximal ideal $\mathfrak{m}R_\mathfrak{m}$ is generated by two elements

### Answers (25)

 5 How to compute $=\lim_{n \to \infty} \Big( \frac{\log{(n+1)}}{\log{(n)}} \cdot \frac{n-2}{n-1} \Big)$“by hand”? 5 How many four digit numbers are there such that its digits strictly ascending? 3 Proving Fermat's Little Theorem with Lagrange 3 Finding the max value of a trigonometric expression 2 Probability that the sum of 6 dice rolls is even

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 6 combinatorics × 2 3 real-analysis × 6 5 elementary-number-theory × 3 3 probability × 5 5 limits × 3 3 trigonometry × 2 5 logarithms 2 dice 4 abstract-algebra × 27 1 ring-theory × 14

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