# Fun problems with binary operations.

Does anyone know of a book / internet resource containing lots of problems relating to properties of binary operations?

An example of the sort of problem I'm looking for is:

Let * be a binary operation on a set $A$ such that $$\text{for all } x, y \in A, \, x*(y*x)=y.$$ Prove that $$\text{for all } x, y \in A, \, (x*y)*x=y.$$

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There's a chapter on Galois connections between operators and relations in Denecke & Wismath's Universal Algebra and Applications, 2002, though not necessarily exercises, or limited to binary ops. –  alancalvitti Feb 28 '13 at 23:38
The problems at people.emich.edu/phoward/w02/411w2h1.pdf may be below the level you want, but have a look. –  Gerry Myerson Mar 1 '13 at 2:30
books.google.it/… This book contains a lot of proofs of implications between properties of (mainly non associative) binary operations. –  MattAllegro Jan 24 at 22:59