Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On finite division rings


Author: Robert H. Oehmke
Journal: Proc. Amer. Math. Soc. 79 (1980), 174-176
MSC: Primary 17A20
DOI: https://doi.org/10.1090/S0002-9939-1980-0565332-2
MathSciNet review: 565332
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Herein it is shown that the set of right powers of a generic element of a finite division ring contains a basis of the ring as an algebra over a prime field. This result is then applied to finite flexible division rings of characteristic not 2 to obtain commutativity.


References [Enhancements On Off] (What's this?)

  • [1] A. A. Albert, On nonassociative division algebras, Trans. Amer. Math. Soc. 72 (1952), 296-309. MR 0047027 (13:816d)
  • [2] H. Braun and M. Koecher, Jordan-Algebren, Springer-Verlag, Berlin, 1966. MR 0204470 (34:4310)
  • [3] N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., vol. 39, Amer. Math. Soc., Providence, R. I., 1968. MR 0251099 (40:4330)
  • [4] D. Knuth, Finite semifields and projective planes, J. Algebra 2 (1965), 182-217. MR 0175942 (31:218)
  • [5] S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 0197234 (33:5416)
  • [6] K. McCrimmon, A note on finite division rings, Proc. Amer. Math. Soc. 17 (1966), 1173-1177. MR 0204479 (34:4319)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17A20

Retrieve articles in all journals with MSC: 17A20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565332-2
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society