- Albert , A.A. 1942 . Quadratic forms permitting composition . Anal. Math. , 43 : 161 – 177 .
- Brown , R. 1967 . On generalized Cayley-Dickson algebras . Pacific J. Math. , 20 : 415 – 422 .
- Chein , Orin and Goodaire , Edgar G. 1986 . Loops whose loop rings are alternative . Comm. Algebra , 14 ( 2 ) : 293 – 310 .
- Chein , Orin and Goodaire , Edgar G. 1988 . Is a right alternative loop ring alternative? . Algebras Groups Geom. , 5 : 297 – 304 .
- Chein , Orin and Goodaire , Edgar G. 1990 . Loops whose loop rings in characteristic 2 are alternative . Comm. Algebra , 18 ( 3 ) : 659 – 688 .
- Chein , Orin . 1974 . Moufang loops of small order I. . Trans. Amer. Math. Soc. , 188 : 31 – 51 .
- Chein , Orin . 1978 . Moufang loops of small order . Mem. Amer. Math. Soc. , 13 ( 197 )
- Chein , O. , Pflugfelder , H. O. and Smith , J.D.H. , eds. 1990 . Quasigroups and loops: theory and applications. , Berlin : Heldermann Verlag .
- de Barros , Luiz. G. X. 1993 . Isomorphisms of rational loop algebras . Comm. Algebra , 21 : 3977 – 3993 .
- de Barros , Luiz. G. X. and Juriaans , Stanley O. 1996 . Units in integral loop rings . J. Algebra , 183 : 637 – 648 .
- Dickson , L. E. 1919 . On quaternions and their generalization and the history of the eight square theorem. . Anal. Math. , 20 : 151 – 171 .
- Eakin , P. and Sathaye , A. 1990 . On automorphisms and derivations of Cayley-Dickson algebras . J. Algebra , 129 ( 2 ) : 263 – 278 .
- Goodaire , E. G. , Jespers , E. and Polcino Milies , C. 1996 . “ Alternative Loop Rings ” . In Elsevier , Amsterdam : North-Holland .
- Goodaire , E. G. , May , Sean and Raman , Maitreyi . 1999 . The Moufang Loops of Order less than 64. , Commack, New York : Nova Science Publishers, Inc. .
- Goodaire , Edgar. G. 1983 . Alternative loop rings , Vol. 30 , 31 – 38 . Publ. Math. Debrecen .
- Goodaire , Edgar. G. 1987 . Circle loops of radical alternative rings . Algebras Groups Geom. , 4 : 461 – 474 .
- Goodaire , Edgar. G. and Parmenter , M. M. 1986 . Units in alternative loop rings . Israel J. Math. , 53 ( 2 ) : 209 – 216 .
- Goodaire , Edgar. G. and Robinson , D. A. 1995 . A class of loops whose loop rings are strongly right alternative . Comm. Algebra , 22 ( 14 ) : 5623 – 5634 .
- Jacobson , Nathan . 1980 . Basic Algebra II. , San Francisco : W. H. Freeman and Company .
- Jespers , E. , Leal , G. and Polcino Milies , C. 1995 . Classifying indecomposable RA loops . J. Algebra , 176 : 5057 – 5076 .
- Pflugfelder , H. O. 1990 . Quasigroups and loops: Introduction , Berlin : Heldermann Verlag .
- Schafer , R. D. 1966 . An introduction to nonassociative algebras , New York : Academic Press .
- Zhevlakov , K. A. , Slin'ko , A. M. , Shestakov , I. P. and Shirshov , A. I. 1982 . Rings that are nearly associative. , New York : Academic Press . translated by Harry F. Smith
Cayley-dickson algebras and RA loops
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.