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On the center of a left Jordan groupoid. (English) Zbl 0944.06005

The author shows that for an associative \(^\ast \)ring with identity the centers of the orthomodular poset of idempotents and of the left Jordan groupoid of idempotents (with the operation \(p \circ q = p - 2pq - 2qp + 4qpq\)) coincide. It is proved that the center of a left Jordan groupoid is an associative subgroupoid.

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
17C50 Jordan structures associated with other structures
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References:

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