6 problems.
- The nilradical is the intersection of all primes; \(N(\mathbb{Z}/(m))\) and \(N(\mathbb{C}[x,y]/(y^2-x^3))\)
- No simple group of order \(30\), and simple groups of order \(60\) are isomorphic to \(A_5\)
- Galois group and intermediate fields of \(\mathbb Q(\zeta_{12})/\mathbb Q\)
- Whether \(\mathbb{Z}[x]/(x^2+x+1)\) is Noetherian, Artinian, or an integrally closed domain
- Irreducible representations of \(\mathrm{GL}_2(\mathbb{F}_2)\), and reducibility of the adjoint representation in order \(12\)
- A commutative integral domain is a field if and only if it is semisimple if and only if every module is projective