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

Let $\mathfrak B$ be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity $((((x_1,x_2),x_3),((x_4,x_5),x_6)),(x_7,x_8))=0$ ($((x_1x_2\cdot x_3)(x_4x_5\cdot x_6))(x_7x_8)=0$, respectively). In this paper, we construct infinite independent systems of identities in the variety $\mathfrak B$ ($\mathfrak D$ , respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety $\mathfrak B$ has the cardinality of the continuum and that there are algebras in $\mathfrak B$ with undecidable word problem.