Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493148 | Journal of Algebra | 2005 | 10 Pages |
Abstract
We study the following question in this paper: If p is a prime, m a positive integer, and S=(sm,â¦,s1) an arbitrary sequence consisting of “Y” or “N,” does there exist a division algebra of exponent pm over a valued field (F,v) such that the underlying division algebra of the tensor power Dâpi has a valuation extending v if and only if smâi=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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Patrick J. Morandi, B.A. Sethuraman,