### Questions (30)

 5 Is the Artinian property dual to the Noetherian property? 5 Q Exercise 4, Hecke Algebras - Daniel Bump 5 Incomparability of Prime ideals in integral Ring Extensions 5 Finite Dimensional algebras over the rationals, with simple modules of arbitrary dimension over the rationals 3 Correspondance between finite index subgroups of $\mathbb{Z}^{2}$ and regular coverings of the Torus

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 +2 Matrix - Linear algebra problem +2 characters of symmetric and exterior algebras +2 Unit cirle through Riemann Zeta Function +2 Relation between $\operatorname{trace}(AB)$ and $\operatorname{trace}(ABAB)$

### Answers (22)

 4 Demonstration of a topic via an example - Representation theory 4 An example needed of Schur's lemma 4 Explanation of a theorem 4 Proving the Fibonacci identity $(−1)^{m−k}(F_{m+k+1}F_{m−k−1}−F_{m+k}F_{m−k}) =F_{k}^2+F_{k+1}^2$ 3 $\langle \chi,\chi \rangle \ge 1$ for any representation

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 17 representation-theory × 17 4 induction 7 abstract-algebra × 10 4 discrete-mathematics 4 linear-algebra × 8 4 fibonacci-numbers 4 sequences-and-series × 3 3 group-theory × 10 4 recurrence-relations × 3 3 finite-fields × 4

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