On local algebras of maximal algebras of Jordan quotients. (English) Zbl 1465.17026
Ortegon Gallego, Francisco (ed.) et al., Recent advances in pure and applied mathematics. Based on contributions presented at the Second Joint Meeting Spain-Brazil in Mathematics, Cádiz, Spain, December 11–14, 2018. Cham: Springer. RSME Springer Ser. 4, 49-59 (2020).
Let \(J\) be a strongly prime Jordan algebra over a unital commutative ring \(\Phi\). In analogy with the case of associative algebras one can form the (Jordan) algebra of quotients \(Q=Q(J)\) of \(J\). The authors work with maximal algebras of quotients and their localizations at nonzero elements of \(J\). They require that the corresponding nonzero element becomes von Neumann regular in the maximal algebra of quotients. The main result of the paper under review is as follows. The authors prove that the constructions of such a local algebra commutes with that of the maximal algebra of quotients. As a corollary to this theorem they obtain that in the case of a strongly prime Jordan algebra, the maximal algebras of quotients with nonzero local PI algebras are rationally primitive.
For the entire collection see [Zbl 1445.37001].
For the entire collection see [Zbl 1445.37001].
Reviewer: Plamen Koshlukov (Campinas)
MSC:
| 17C10 | Structure theory for Jordan algebras |
| 17C20 | Simple, semisimple Jordan algebras |
| 17C99 | Jordan algebras (algebras, triples and pairs) |
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