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

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The book by R. D. Schafer starts with a chapter at that generality. –  Mariano Suárez-Alvarez Apr 3 '13 at 20:47

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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")

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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.

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