The Malcev algebra associated to a power-associative algebra

In this work, we examine the construction of a Malcev algebra by employing the product of a commutative power-associative nilalgebra [Formula: see text] of nilindex four, with an element whose square is zero. Notably, when [Formula: see text] is associative, the resulting algebra exhibits a trivial product structure. On the other hand, if [Formula: see text] is a Jordan algebra, the associated algebra is a nilpotent Lie algebra with a nilindex strictly less than four. More broadly, in the general case, the Malcev algebra derived through this construction remains nilpotent, with a solvable index that does not exceed three.