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Summary: Journal of Algebra 223, 527534 (2000)
doi:10.1006/jabr.1999.8057, available online at http://www.idealibrary.com on
Exponent Reduction for Radical Abelian Algebras1
Eli Aljadeff and Jack Sonn
Department of Mathematics, Technion, 32000 Haifa, Israel
E-mail: aljadeff@math.technion.ac.il, sonn@math.technion.ac.il
Communicated by A. Lubotzky
Received September 10, 1998
Let k be a field. A radical abelian algebra over k is a crossed product K/k ,
where K = k T is a radical abelian extension of k, T is a subgroup of K
which
is finite modulo k
, and H2
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 k k µ , where µ 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. © 2000 Academic Press
1. INTRODUCTION AND SUMMARY OF RESULTS
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