TITLE: Counterexamples in algebra
QUESTION [8 upvotes]: I got the feeling that whenever a subject gets so sophisticated that Zorn's lemma is needed, a book of counterexamples in that subject would probably benefit researchers/ students a lot. 
Zorn's lemma definitely appears a lot in abstract algebra, and I often find myself thinking about statements I can neither find a proof nor counterexamples. This is fun but sometimes it could be time consuming.
Therefore I wonder whether there is a book of counterexamples in algebra, or just a nice collection of them somewhere. Maybe algebra is too large a subject, so such a collection from sub-subject (field theory, modules, etc) is also welcome.
Thanks!
As mentioned in the comment, there is a nice list on M.O. However, that list is a little bit random. I am looking for something that might be more systematic if less instructional.

REPLY [3 votes]: If you do a search in Amazon for "consequences of the axiom of choice",
the first responses are:
Consequences of the Axiom of Choice (Mathematical Surveys and Monographs) by Paul Howard ($108.00)
The Axiom of Choice (Dover Books on Mathematics) by Thomas J. Jech ($11.05, also Kindle)
Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Dover Books on Mathematics) by Gregory H. Moore ($14.44)