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Proceedings of the American Mathematical Society

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



Noncrossed products of small exponent

Author: David J. Saltman
Journal: Proc. Amer. Math. Soc. 68 (1978), 165-168
MSC: Primary 16A40
MathSciNet review: 0476794
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Abstract: Using the generic division algebras, we construct new division algebras and prove the following. Theorem. Let $ m$, $ n$ be positive integers, $ m\vert n$, such that $ m$ is divisible by every prime which divides $ n$. If $ k$ is any field, and there is a prime $ p$ such that $ {p^3}\vert m$, then there is a noncrossed product division $ k$-algebra of exponent $ m$ and degree $ n$. If $ k$ is a global field of characteristic 0, $ p$ is an odd prime, and $ k$ does not contain a primitive $ p$th root of 1, we need only assume $ p^2\vert m$.

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Keywords: Division algebra, crossed product
Article copyright: © Copyright 1978 American Mathematical Society