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.



Titolo: On the classification of centrally finite alternative division rings satisfying algebraic closure conditions
Autori: Riccardo Ghiloni
Autori Unitn: 
Ghiloni, Riccardo
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 ISI: WOS:000309362700008
Digital Object Identifier (DOI): 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)

File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
 
 
 
Powered by IRIS-about IRIS-Utilizzo dei cookie
Logo CINECA  Copyright © 2020