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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maximal subalgebras of central separable algebras


Author: M. L. Racine
Journal: Proc. Amer. Math. Soc. 68 (1978), 11-15
MSC: Primary 16A16
MathSciNet review: 0453796
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Abstract: Let A be a central separable algebra over a commutative ring R. A proper R-subalgebra of A is said to be maximal if it is maximal with respect to inclusion.

Theorem. Any proper subalgebra of A is contained in a maximal one. Any maximal subalgebra B of A contains a maximal ideal $ \mathfrak{m}A$ of A, $ \mathfrak{m}$ a maximal ideal of R, and $ B/\mathfrak{m}A$ is a maximal subalgebra of the central simple $ R/\mathfrak{m}$ algebra $ A/\mathfrak{m}A$.

More intrinsic characterizations are obtained when R is a Dedekind domain.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0453796-5
Keywords: Central separable algebra, maximal subalgebra, Dedekind domain
Article copyright: © Copyright 1978 American Mathematical Society