MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Any results or concise introduction about nonassociative algebra that even does not satisify Power associativity?

share|cite|improve this question
The book by R. D. Schafer starts with a chapter at that generality. – Mariano Suárez-Alvarez Apr 3 '13 at 20:47
There are lots of results about particular classes of algebras that are not power associative. For example, Leibniz algebras, Evolution algebras, Bernstein algebras, antiflexible algebras. A generalisation called Hom-power associative algebras has been introduced by Yau. – David Towers Oct 25 '15 at 17:33
up vote 1 down vote accepted

K.Zhevlakov, A.Slin'ko, I.Shestakov, A.Shirshov, Rings that are nearly associative. Academic Press, 1982 (Chapt.1)

P.Cohn, Universal algebra, Harper and Row, 1965 (Chapt.7, Sec.5 "Linear algebras")

share|cite|improve this answer

Jean-Louis Loday, Bruno Vallette "Algebraic operads", Grundlehren Math. Wiss. 346, Springer, Heidelberg, 2012. This book also has a lot of information on nonassociative algebras. Many interesting nonassociative algebras are described in Lodays article "ENCYCLOPEDIA OF TYPES OF ALGEBRAS 2010", written under the name of G. W. ZINBIEL. Here ZINBIEL referres to LEIBNIZ (algebras) backwards.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.