Abstract
It is shown that every associative triple system M of the second kind (see below for the definition) may be imbedded into an associative algebra A with involution J in such a way that 〈xyz〉=xJ(y)z. We define the radical of M and study its relation with the radical of A. Finally we classify the finite-dimensional semisimple associative triple systems over a field.
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Loos, O. Assoziative tripelsysteme. Manuscripta Math 7, 103–112 (1972). https://doi.org/10.1007/BF01679707
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DOI: https://doi.org/10.1007/BF01679707