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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Primitive ideals in von Neumann algebras


Author: Herbert Halpern
Journal: Proc. Amer. Math. Soc. 39 (1973), 563-566
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1973-0318906-4
MathSciNet review: 0318906
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Abstract: For a von Neumann algebra it is shown that the set of primitive ideals containing a fixed maximal ideal of the center is sequentially closed in the order topology defined on the set of all ideals containing the maximal ideal. As a corollary, it is shown that every ideal generated by a sequence of elements of a von Neumann algebra and a maximal ideal of the center is either primitive or simple modulo a primitive ideal.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318906-4
Keywords: von Neumann algebra, primitive ideal
Article copyright: © Copyright 1973 American Mathematical Society