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COMMUTATIVE JORDAN NILALGEBRAS OF NILINDEX 4 GENERATED BY AT MOST THREE ELEMENTS
Keywords:
commutative nilalgebras, Jordan algebras, Engel's algebrasAbstract
The present study is about commutative Jordan nilalgebras of nilindex 4 generated by at most three elements over a field K of characteristic $\neq 2,3$. We first look at the case where such algebras are generated by two elements and satisfy Engel’s third or fourth condition, then we consider the case where they are generated by three elements and satisfy Engel’s third condition. We prove that these algebras are nilpotent, and hence solvable, while giving a bound of the index of solvability and nilpotency.
Received: October 7, 2022
Revised: December 5, 2022
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