Non-cyclic algebras with -central elements

Authors:
Eliyah Matzri , Louis H. Rowen and Uzi Vishne
Journal:
Proc. Amer. Math. Soc. 140 (2012), 513-518
MSC (2010):
Primary 16K20
Published electronically:
August 11, 2011
MathSciNet review:
2846319
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Abstract: We construct, for any prime , a non-cyclic central simple algebra of degree with -central elements. This construction answers a problem of Peter Roquette.

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Bibliography
1. A.A. Albert, Non-cyclic algebras with pure maximal subfields , Bull. AMS 44 , 576-579 (1938). MR 1563796
2. A.A. Albert, Modern Higher Algebra, University of Chicago Press, 1937.
3. A.A. Albert, Structure of Algebras, Amer. Math. Soc. Coll. Publ. XXIV , AMS, 1961. MR 0123587 (23:A912)
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5. R. Dubisch, Non-cyclic algebras of degree four and exponent two with pure maximal subfields , Bull. Amer. Math. Soc. 47 , 131-133 (1941). MR 0003623 (2:246b)
6. A. Auel, E. Brussel, S. Garibaldi and U. Vishne, Open problems on central simple algebras , Transformation Groups 16 (1), 219-264 (2011).
7. J. Minác and A. Wadsworth, Division algebras of prime degree and maximal Galois -extensions , Canad. J. Math. 59 (3), 658-672 (2007). MR 2319163 (2008c:16029)
8. U. Vishne, Galois cohomology of fields without roots of unity , J. Algebra 279 (2), 451-492 (2004). MR 2078127 (2005e:12008)
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Additional Information
Eliyah Matzri
Affiliation:
Department of Mathematics, The Technion, Haifa 32000, Israel
Email:
elimatzri@gmail.com
Louis H. Rowen
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
Email:
rowen@math.biu.ac.il
Uzi Vishne
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
Email:
vishne@math.biu.ac.il
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11236-X
Received by editor(s):
September 6, 2010
Received by editor(s) in revised form:
December 5, 2010
Published electronically:
August 11, 2011
Communicated by:
Harm Derksen
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.