Algebra notes

Please keep in mind that most of these texts have never been proofread. (One day I realized that proofreading my own proofs took me way more time than writing them, and sometimes even more time than finding them.) Should you find any mistakes or have any other remarks, I will be very glad to hear about them (my email address is, where A = darijgrinberg and B = gmail).
Notes taken in lectures:
Papers (publications and preprints):
Other writings:
Sidenotes to Michiel Hazewinkel: Witt vectors. Part 1:

Witt vectors reside somewhere on the crossroads between algebra, combinatorics and number theory. Hazewinkel's text is, in my opinion, a must-read for everyone interested in at least two of these fields. It also sheds light on the representation theory of symmetric groups, the theory of symmetric polynomials, Hopf algebras and λ-rings.

I tend to advise Hazewinkel's text to anyone interested in any of the subjects mentioned, due to its very vivid and explanatory writing style. (It was the main thing that made me study combinatorial algebra!) Unfortunately, a multitude of typos makes reading it harder than it should be. If you have troubles with understanding something in the text, the reason may be in this list of errata (plus a few remarks). (Here is a more complete collection of errata which I sent to the author; these include obvious spelling mistakes which won't hinder anyone at understanding the text.)
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Here are some sidenotes I have made. Usually, these contain proofs of assertions which are mentioned without proof in Hazewinkel's work. Some contain generalizations/extensions (however, it's mostly the cheap kind of generalization, that barely adds any new content). I have written them for myself to keep track of what's true and what isn't; unfortunately they aren't very readable... LaTeX sourcecode of the above.

Sidenotes to Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina: Introduction to representation theory:

Errata to various books and papers:

When reading mathematics, I tend to keep track of errors and places that I don't understand by taking notes on the sides. In some cases, when I suspect that my notes might possibly be of some use to others, I put them online here.

Caveat lector: Do not take my lists of errata at face value. There is no guarantee that what I claim to be errors are actually errors, nor that what I believe to be corrections is more correct than the originals.

Further plans (outdated):

Algebra notes

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Darij Grinberg