In this paper, we prove that the rings of quaternions and of octonions over an arbitrary real closed field are algebraically closed in the sense of Eilenberg and Niven. As a consequence, we infer that some reasonable algebraic closure conditions, including the one of Eilenberg and Niven, are equivalent on the class of centrally finite alternative division rings. Furthermore, we classify centrally finite alternative division rings satisfying such equivalent algebraic closure conditions: up to isomorphism, they are either the algebraically closed fields or the rings of quaternions over real closed fields or the rings of octonions over real closed fields.
On the classification of centrally finite alternative division rings satisfying algebraic closure conditions / Riccardo Ghiloni. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - STAMPA. - 11:5(2012), pp. 1250088-1-1250088-13.
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Titolo: | On the classification of centrally finite alternative division rings satisfying algebraic closure conditions | |
Autori: | Riccardo Ghiloni | |
Autori Unitn: | ||
Titolo del periodico: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS | |
Anno di pubblicazione: | 2012 | |
Numero e parte del fascicolo: | 5 | |
Codice identificativo Scopus: | 2-s2.0-84866666885 | |
Codice identificativo WOS: | WOS:000309362700008 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S0219498812500880 | |
Handle: | http://hdl.handle.net/11572/90543 | |
Citazione: | On the classification of centrally finite alternative division rings satisfying algebraic closure conditions / Riccardo Ghiloni. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - STAMPA. - 11:5(2012), pp. 1250088-1-1250088-13. | |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |