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Abstract and Applied Analysis
Volume 6 (2001), Issue 1, Pages 1-11
http://dx.doi.org/10.1155/S1085337501000458

Douglas algebras without maximal subalgebra and without minimal superalgebra

University of Louisiana at Lafayette, Lafayette, LA 70504, USA

Received 25 February 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give several examples of Douglas algebras that do not have any maximal subalgebra. We find a condition on these algebras that guarantees that some do not have any minimal superalgebra. We also show that if A is the only maximal subalgebra of a Douglas algebra B, then the algebra A does not have any maximal subalgebra.