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The Frattini subalgebra of a Bernstein algebra*
Published online by Cambridge University Press: 20 January 2009
Abstract
Let A be a finite-dimensional Bernstein algebra over a field K with characteristic not 2. Maximal subalgebras of A are studied, and they are determined if A is a genetic algebra. It is also proved that the intersection of all maximal subalgebras of A (the Frattini subalgebra of A) is always an ideal. Finally the structure of Bernstein algebras with Frattini subalgebra equal to zero is described.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 397 - 403
- Copyright
- Copyright © Edinburgh Mathematical Society 1992
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