TY - JOUR

T1 - Exponent reduction for radical abelian algebras

AU - Aljadeff, Eli

AU - Sonn, Jack

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

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

VL - 223

SP - 527

EP - 534

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -