Simple right-symmetric \((1, 1)\)-superalgebras. (English. Russian original) Zbl 1515.17012
Algebra Logic 60, No. 2, 108-114 (2021); translation from Algebra Logika 60, No. 2, 166-175 (2021).
Summary: It is proved that 2-torsion-free simple right-symmetric superrings having a nontrivial idempotent and satisfying a superidentity \((x, y, z) + (-1)^{z(x+y)}(z, x, y) + (-1)^{x(y+z)}(y, z, x) = 0\) are associative. As a consequence, every simple finitedimensional \((1, 1)\)-superalgebra with semisimple even part over an algebraically closed field of characteristic 0 is associative.
MSC:
| 17A70 | Superalgebras |
Keywords:
right-symmetric ring; left-symmetric algebra; pre-Lie algebra; simple ring; Peirce decomposition; \((1, 1)\)-superalgebraReferences:
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