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On a multiplication decomposition theorem in a Dedekind $ \sigma $-complete partially ordered linear algebra


Author: Taen Yu Dai
Journal: Proc. Amer. Math. Soc. 44 (1974), 12-16
MSC: Primary 06A70
DOI: https://doi.org/10.1090/S0002-9939-1974-0335393-1
MathSciNet review: 0335393
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Abstract: Suppose a Dedekind $ \sigma $-complete partially ordered linear algebra (dsc-pola) satisfies a certain multiplication decomposition property (see definition below), then we show that this partially ordered linear algebra actually has the same structure of a special class of real matrix algebras, consisting of elements that can be decomposed as diagonal part plus nilpotent part $ w$, such that $ {w^2} = 0$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0335393-1
Keywords: Dedekind $ \sigma $-complete partially ordered linear algebra, nilpotent, multiplication decomposition property, matrix inequalities
Article copyright: © Copyright 1974 American Mathematical Society

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