TY - JOUR
T1 - Exponent reduction for radical abelian algebras
AU - Aljadeff, Eli
AU - Sonn, Jack
N1 - Funding Information:
1This research was supported by the Fund for the Promotion of Research at the Technion and the Technion VPR Fund.
PY - 2000/1/15
Y1 - 2000/1/15
N2 - Let k be a field. A radical abelian algebra over k is a crossed product (K/k,α), where K=k(T) is a radical abelian extension of k, T is a subgroup of K* which is finite modulo k*, and α∈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⊗kk(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.
AB - Let k be a field. A radical abelian algebra over k is a crossed product (K/k,α), where K=k(T) is a radical abelian extension of k, T is a subgroup of K* which is finite modulo k*, and α∈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⊗kk(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.
UR - http://www.scopus.com/inward/record.url?scp=0034649937&partnerID=8YFLogxK
U2 - 10.1006/jabr.1999.8057
DO - 10.1006/jabr.1999.8057
M3 - 文章
AN - SCOPUS:0034649937
SN - 0021-8693
VL - 223
SP - 527
EP - 534
JO - Journal of Algebra
JF - Journal of Algebra
IS - 2
ER -