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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ideals of multiplier algebras of simple AF $ C\sp *$-algebras


Author: Hua Xin Lin
Journal: Proc. Amer. Math. Soc. 104 (1988), 239-244
MSC: Primary 46L05; Secondary 46M10
MathSciNet review: 958075
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Abstract: It is shown that the $ {C^ * }$-algebra $ M(A)/A$, where $ A$ is a nonunital separable simple AF $ {C^ * }$-algebra and $ M(A)$ is the multiplier algebra of $ A$, is simple if and only if $ A$ has a continuous scale or $ A$ is elementary. Some results concerning the ideal structure of $ M(A)/A$ are also obtained in the case that it is nontrivial.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958075-1
PII: S 0002-9939(1988)0958075-1
Keywords: Simple AF $ {C^ * }$-algebra, ideal, multipliers
Article copyright: © Copyright 1988 American Mathematical Society