December 31, 2010

The major change in the past few days is the addition of a section on Galois theory, which was recently donated. As a result, the chapter on fields has expanded somewhat.

The chapter on flatness has expanded slightly (with sections on the local and infinitesimal criteria).

Various snippets of code donated (e.g. problem sets) have been moved into the main document, often as worked examples (such as the computation of the radical of a polynomial ring $R[x]$ in terms of the radical of $R$).

There is now a section discussing a general observation (due to Lam and Reyes) that ideals maximal with respect to a certain property (e.g. being not finitely generated) are often prime.

Importantly for those editing the source, the package ntheorem has now replaced amsthm in the document. Hopefully this will allow for auto-generated theorem lists eventually. In addition, the package cleveref is now used, so that references of the form “Theorem~\ref{name}” can be simplified to “\cref{name}.” This also provides greater versatility if we want to change theorems into propositions or vice versa.

Finally, the book is nearing 300 pages!

1. Nice.