Abstract
In this paper we deal with the variety of commutative algebras satisfying the identity \(\beta \{(yx^2)x-(yx\cdot x)x\}+\gamma \{y(x^2x)-(yx\cdot x)x\}=0\), where \(\beta , \gamma \) are scalars. They are called generalized almost-Jordan algebras. We show under some conditions that generalized almost-Jordan algebras contain an idempotent. We revisit the study of these algebras. We show particularly that they contain an associative subalgebra with a unity. Thus, when the algebra is simple, it is an associative field. The special cases \(\beta =0\), \(\gamma =0\), \(\beta +2\gamma =0\) and \(\beta +\gamma =0\) have been studied. In each case we give examples.
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Dembega, A., Ouattara, M. Generalized almost-Jordan algebras. Afr. Mat. 31, 167–175 (2020). https://doi.org/10.1007/s13370-018-0612-2
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DOI: https://doi.org/10.1007/s13370-018-0612-2