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Journal of Algebra 223, 527534 (2000) doi:10.1006/jabr.1999.8057, available online at http://www.idealibrary.com on
 

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 , where 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

  

Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology

 

Collections: Mathematics