Valuations on Tensor Powers of a Division Algebra
نویسنده
چکیده
We study the following question in this paper: If p is a prime, m a positive integer, and S = (sm, . . . , s1) an arbitrary sequence consisting of “Y ”or “N”, does there exist a division algebra of exponent p over a valued field (F, v) such that the underlying division algebra of the tensor power D⊗p i has a valuation extending v if and only if sm−i = Y ? We show that if such an algebra exists, then its index must be bounded below by a power of p that depends on both m and S, and we then answer the question affirmatively by constructing such an algebra of minimal index.
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