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Title
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Symbol length in positive characteristic
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Author
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Abstract
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| We show that any central simple algebra of exponent p in prime characteristic p that is split by a p-extension of degree p(n) is Brauer equivalent to a tensor product of 2 center dot p(n-1) -1 cyclic algebras of degree p. If p = 2 and n >= 3, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of 5 center dot 2n-3 -1 quaternion algebras. Furthermore, we provide new proofs for some bounds on the minimum number of cyclic algebras of degree p that is needed to represent Brauer classes of central simple algebras of exponent p in prime characteristic p, which have previously been obtained by different methods. (c) 2024 Elsevier B.V. All rights reserved. |
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Language
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English
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Source (journal)
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Journal of pure and applied algebra. - Amsterdam
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Publication
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Amsterdam
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2024
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ISSN
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0022-4049
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DOI
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10.1016/J.JPAA.2024.107613
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Volume/pages
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228
:6
(2024)
, p. 1-10
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Article Reference
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107613
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ISI
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001172339600001
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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