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The Frattini subalgebra of a Bernstein algebra*

Published online by Cambridge University Press:  20 January 2009

Jesús Laliena
Jesús Laliena
Affiliation:
Colegio Universitario de la RiojaC/Obispo Bustamante 326001–LogroñoSpain
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Abstract

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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

References

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