Commutative Algebra
A non-comprehensive collection of solutions to Atiyah-Macdonald’s exercises, with some additional comments and discussions. There may be errors, for reference only.
On Hilbert’s Nullstellensatz and the ideal–variety correspondence.
Thanks to the powerful tools borrowed from commutative algebra, we show a general approach to determine the prime spectra of some coordinate rings by examples. As we determine the spectrum of the Gaussian integers, a proof of the famous two squares theorem emerges without tricky techniques.
