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Exponent Reduction for Radical Abelian Algebras

✍ Scribed by Eli Aljadeff; Jack Sonn

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
83 KB
Volume
223
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let k be a field. A radical abelian algebra over k is a crossed product K/k Ξ± , where K = k T is a radical abelian extension of k, T is a subgroup of K * which is finite modulo k * , and Ξ± ∈ H 2 G K * is represented by a cocycle with values in T . The main result is that if A is a radical abelian algebra over k, and m = exp A βŠ— k k Β΅ , where Β΅ denotes the group of all roots of unity, then k contains the mth roots of unity. Applications are given to projective Schur division algebras and projective Schur algebras of nilpotent type.

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