Algebras whose right nucleus is a central simple algebra
| Autor: | Susanne Pumplün |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Jordan algebra Quaternion algebra Splitting field 010102 general mathematics Mathematics - Rings and Algebras Primary extension 01 natural sciences 010101 applied mathematics Rings and Algebras (math.RA) Field extension FOS: Mathematics Division algebra 0101 mathematics Algebraically closed field Central simple algebra 17A35 (Primary) 17A60 16S36 (Secondary) Mathematics |
| ISSN: | 0022-4049 |
| Popis: | We generalize Amitsur's construction of central simple algebras over a field $F$ which are split by field extensions possessing a derivation with field of constants $F$ to nonassociative algebras: for every central division algebra $D$ over a field $F$ of characteristic zero there exists an infinite-dimensional unital nonassociative algebra whose right nucleus is $D$ and whose left and middle nucleus are a field extension $K$ of $F$ splitting $D$, where $F$ is algebraically closed in $K$. We then give a short direct proof that every $p$-algebra of degree $m$, which has a purely inseparable splitting field $K$ of degree $m$ and exponent one, is a differential extension of $K$ and cyclic. We obtain finite-dimensional division algebras over a field $F$ of characteristic $p>0$ whose right nucleus is a division $p$-algebra. Some minor changes to previous version, some definitions added in Section 2 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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