Identities of the algebra 𝕆⊗𝕆

Abstract

We find nonassociative polynomial identities of minimal degree, which is 7 7 , for the algebras O ⊗ O {\mathbb {O}}{\otimes _{}}{\mathbb {O}} and M 2 ( O ) {\operatorname {M}_{2}}({\mathbb {O}}) , where O {\mathbb {O}} is the octonion algebra.