Douglas algebras without maximal subalgebra and without minimal superalgebra
Guillory, Carroll
Abstr. Appl. Anal., Tome 6 (2001) no. 1, p. 1-11 / Harvested from Project Euclid
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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.
Publié le : 2001-05-14
Classification:  46J15 
@article{1050266655,
     author = {Guillory, Carroll},
     title = {Douglas algebras without maximal subalgebra and without
 minimal superalgebra},
     journal = {Abstr. Appl. Anal.},
     volume = {6},
     number = {1},
     year = {2001},
     pages = { 1-11},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050266655}
}

Guillory, Carroll. Douglas algebras without maximal subalgebra and without
 minimal superalgebra. Abstr. Appl. Anal., Tome 6 (2001) no. 1, pp.  1-11. http://gdmltest.u-ga.fr/item/1050266655/