## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Common subfields of $p$-algebras of prime degree

#### Abstract

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

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

Dates
First available in Project Euclid: 18 November 2015

https://projecteuclid.org/euclid.bbms/1447856067

Mathematical Reviews number (MathSciNet)
MR3429179

Zentralblatt MATH identifier
1367.16015

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

#### Citation

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