Bulletin of the Belgian Mathematical Society - Simon Stevin

Common subfields of $p$-algebras of prime degree

Adam Chapman

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We prove that if two division $p$-algebras of prime degree share an inseparable field extension of the center then they also share a cyclic separable one. We show that the converse is in general not true. We also point out that sharing all the inseparable field extensions of the center does not imply sharing all the cyclic separable ones.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 4 (2015), 683-686.

First available in Project Euclid: 18 November 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16K20: Finite-dimensional {For crossed products, see 16S35}

Central Simple Algebras Cyclic Algebras p-Algebras Linkage Division Algebras


Chapman, Adam. Common subfields of $p$-algebras of prime degree. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 4, 683--686. https://projecteuclid.org/euclid.bbms/1447856067

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