Exponent reduction for radical abelian algebras

Eli Aljadeff*, Jack Sonn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)527-534
Number of pages8
JournalJournal of Algebra
Volume223
Issue number2
DOIs
StatePublished - 15 Jan 2000
Externally publishedYes

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