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

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