Carroll Guillory, "Douglas algebras without maximal subalgebra and without minimal superalgebra", Abstract and Applied Analysis, vol. 6, Article ID 620768, 11 pages, 2001. https://doi.org/10.1155/S1085337501000458
Douglas algebras without maximal subalgebra and without minimal superalgebra
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 is the only maximal subalgebra of a Douglas algebra , then the algebra does not have any maximal subalgebra.
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