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The Jordan regular ring associated to a finite JBW-algebra. (English) Zbl 0623.46032
S. K. Berberian [Ann. Math., II. Ser. 65, 224-240 (1957; Zbl 0085.099)] showed that a finite \(AW^*\)-algebra A can be embedded in a continuous *-regular ring R such that R has no new self-adjoint idempotents. The authors extend Berberian’s results to a finite JBW- algebra A showing that A can be embedded in a von Neumann regular Jordan ring.
Reviewer: C.M.Edwards

MSC:
46L70 Nonassociative selfadjoint operator algebras
17C65 Jordan structures on Banach spaces and algebras
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