Abstract
The paper is devoted to give an answer about the existence of associative and non-associative Jordan algebras of nilpotency type \(\left( n,1,m\right) \) for any \(n,m\in \mathbb {N} \). According to this answer, we classify (up to isomorphism) all Jordan algebras of nilpotency type \(\left( 2,1,m\right) \) and all commutative associative algebras of nilpotency type \(\left( n,1,m\right) \).
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Hegazi, A.S., Abdelwahab, H. Is it possible to find for any \(\varvec{n,m\in \mathbb {N}}\) a Jordan algebra of nilpotency type \(\varvec{(n,1,m)?}\) . Beitr Algebra Geom 57, 859–880 (2016). https://doi.org/10.1007/s13366-016-0292-8
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DOI: https://doi.org/10.1007/s13366-016-0292-8