Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two

Let be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity ((((x₁,x₂),x₃), ((x₄,x₅),x₆)), (x₇,x₈)) = 0 (((x₁x₂ · x₃)(x₄x₅ · x₆))(x₇x₈) = 0, respectively). In this paper, we construct infinite independent systems of identities in the variety (, respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety has the cardinality of the continuum and that there are algebras in with undecidable word problem.