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)



Cyclic algebras of small exponent

Author: J.-P. Tignol
Journal: Proc. Amer. Math. Soc. 89 (1983), 587-588
MSC: Primary 11R54; Secondary 13A20, 16A16
MathSciNet review: 718978
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every cyclic algebra of exponent $n$ and degree $mn$ over a field containing a primitive $n$th root of unity is similar to a tensor product of at most $m$ symbols of degree $n$.

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

  • A. Adrian Albert, Structure of algebras, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR 0123587
  • A. S. Merkurjev and A. A. Suslin, $K$-cohomology of Severi-Brauer varieties and norm residue homomorphism, preprint, 1981.
  • John Milnor, Introduction to algebraic $K$-theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 72. MR 0349811
  • S. Rosset and J. Tate, A reciprocity law for ${K_2}$-traces, preprint, 1982.
  • Louis Halle Rowen, Central simple algebras with involution viewed through centralizers, J. Algebra 63 (1980), no. 1, 41–55. MR 568563, DOI
  • Jean-Pierre Serre, Corps locaux, Hermann, Paris, 1968 (French). Deuxième édition; Publications de l’Université de Nancago, No. VIII. MR 0354618
  • Edwin Weiss, Cohomology of groups, Pure and Applied Mathematics, Vol. 34, Academic Press, New York-London, 1969. MR 0263900

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R54, 13A20, 16A16

Retrieve articles in all journals with MSC: 11R54, 13A20, 16A16

Additional Information

Keywords: Cyclic algebras, Brauer group of fields
Article copyright: © Copyright 1983 American Mathematical Society