Advanced search
Publication Cover
Communications in Algebra Volume 28, 2000 - Issue 1
Submit an article Journal homepage
50
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Cayley-dickson algebras and alternative loop algebras

Yongxin Zhou Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, A1C 5S7, Canada E-mail: [email protected]View further author information
Pages 523-539 | Received 01 Jul 1998, Published online: 03 Nov 2008

  • Albert , A. A. 1942 . Quadratic forms permitting composition . Anal. Math. , 43 : 161 – 177 .
  • Bruck , R. H. 1958 . A survey of binary systems, volume 20 of Ergeb. Math. Grenzgeb , Springer-Verlag .
  • Chein , Orin and Goodaire , Edgar G. 1986 . Loops whose loop rings are alternative . Comm. Algebra , 14 ( 2 ) : 293 – 310 .
  • 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 . On semisimple alternative loop algebras . Comm. Algebra , 21 : 3995 – 4011 .
  • Dickson , L. E. 1919 . On quaternions and their generalization and the history of the eight square theorem . Anal. Math. , 20 : 151 – 171 .
  • Divinsky , N.J. 1965 . “ Rings and radicals ” . In Number 14 in Mathematical Expositions , Toronto : University of Toronto Press .
  • Goodaire , E. G. , Jespers , E. and Polcino Milies , C. 1996 . “ Alternative Loop Rings ” . In Elsevier , Amsterdam : North-Holland .
  • Goodaire , Edgar 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 Zhou , Yongxin . Cayley-Dickson algebras and RA-Ioops 527 – 544 .
  • Jespers , E. , Wauters , P. and Wauters , P. 1985 . The Brown-McCoy radicals of semigroup rings of commutative cancellative semigroups . Glasgow Math. J. , 26 : 107 – 113 .
  • Karpilovsky , G. 1987 . “ The Jacobson radicals of group algebras ” . In Elsevier , Amsterdam : North-Holland .
  • Pflugfelder , H. O. 1990 . Quasigroups and loops: Introduction. , Berlin : Heldermann Verlag .
  • Sandling , R. 1974 . Group rings of circle and unit groups . Math. Z. , 140 : 195 – 202 .
  • Schafer , R. D. 1966 . An introduction to nonassociative algebras , New York : Academic Press .
  • Szasz , F. 1981 . Radicals of rings , London : J. Wiley .
  • Tuganbaev , A. A. 1992 . Quaternion algebras over local rings . Uspekhi Mat. Nauk , 47 ( 3 ) : 179 – 180 . Translation in Russian Math. Surveys 47 (1992), no. 3,194-195.
  • Tuganbaev , A. A. 1993 . Generalized quaternion algebras . Mat. Zametki , 53 : 120 – 128 . Translated in Math. Notes 53 (1993), no. 5-6, 534-538
  • Yongxin , Zhou . 1995 . The Jacobson and Brown-McCoy radicals of certain group rings . Chinese Quarterly J. Math. , 10 : 91 – 96 .
  • 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

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.