Mathematical Logic Quarterly 39 (1):241-250 (1993)

Abstract
Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10
Keywords AL*‐algebra  Boolean valued analysis  L*‐algebra  Lie algebra  AW*‐module
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DOI 10.1002/malq.19930390128
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Two Applications of Logic to Mathematics.Gaisi Takeuti - 1978 - Princeton University Press.

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