Nonassociative algebra

Summary

A nonassociative algebra over a commutative ring $R$ is an $R$-module with an $R$-bilinear multiplication. The word "nonassociative" means "not necessarily associative", so associative algebras are a special case. The main classes are Lie algebras, Jordan algebras and alternative algebras such as the octonions. Each class is cut out by identities that replace the associative law.