Primitive ideals in von Neumann algebras

Halpern, Herbert

doi:10.1090/S0002-9939-1973-0318906-4

Primitive ideals in von Neumann algebras
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by Herbert Halpern

Proc. Amer. Math. Soc. 39 (1973), 563-566

DOI: https://doi.org/10.1090/S0002-9939-1973-0318906-4

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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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