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A new construction of noncrossed product algebras


Authors: Bill Jacob and Adrian R. Wadsworth
Journal: Trans. Amer. Math. Soc. 293 (1986), 693-721
MSC: Primary 16A39; Secondary 12G05
DOI: https://doi.org/10.1090/S0002-9947-1986-0816320-X
MathSciNet review: 816320
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Abstract: New examples of noncrossed product division algebras are obtained, using methods different from all previous noncrossed product constructions. The examples are division algebras over intersections of $ p$-Henselian valued fields, and they have Schur index $ {p^m}$ and exponent $ {p^n}$ for any prime number $ p$ and any integers $ m \geqslant n \geqslant 2\;(n \geqslant 3\;{\text{if}}\;p = 2)$. The basic tools used in the construction are valuation theory and Galois cohomology; no generic methods are applied and there is no p.i. theory. Along the way, local-global principles are proved for central simple algebras over intersections of $ p$-Henselian valued fields.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0816320-X
Article copyright: © Copyright 1986 American Mathematical Society

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