Nonassociative ring

Summary

A nonassociative ring is an abelian group with a multiplication that distributes over addition on both sides, without the requirement that it be associative. "Nonassociative" means "not necessarily associative", so associative rings are a special case. Lie algebras, Jordan algebras and the octonions are the main examples where associativity fails. A nonassociative algebra over a field is the same notion with a compatible vector space structure.