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Extensions of AH algebras with the ideal property

Published online by Cambridge University Press:  20 January 2009

Cornel Pasnicu
Cornel Pasnicu
Affiliation:
Department of Mathematics and Computer Science, University of Puerto Rico, Box 23355, San Juan PR 00931-3355, U.S.A. E-mail address: cpasnic@upracd.upr.clu.edu
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In this note we show that if we have an exact sequence of AH algebras (AH stands for “approximately homogeneous”) 0 → I → A → B → 0, then A has the ideal property (i.e., any ideal is generated by its projections) if and only if I and B have the ideal property. Also, we prove that an extension of two AT algebras (AT stands for “approximately circle”) with the ideal property is an AT algebra with the ideal property if and only if the extension is quasidiagonal.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 65 - 76
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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