TY - JOUR

T1 - On the decomposition of cyclic algebras

AU - Rowen, L. H.

AU - Tignol, J. P.

PY - 1996/6

Y1 - 1996/6

N2 - A cyclic algebra (K/F, σ, a) of degree n has property D(f) if it decomposes as a tensor product of a cyclic algebra of degree e=n/f containing L (the fixed subfield under σ e) and a cyclic subalgebra of degree f containing a f-th root of a. Although D(2) holds for every cyclic algebra of degree 4 and exponent 2, D(p) fails for Brauer algebras of degree p 2 and exponent p, and D(2) fails for Brauer algebras of degree 8 and exponent 2. Using this, one fills the gap in [6, Theorem 4] and [7, Theorem 7.3.28], to show that the example given there is indeed tensor indecomposable of degree p 2 and exponent p. An easy ultraproduct argument provides an example containing all p k roots of 1, for all k.

AB - A cyclic algebra (K/F, σ, a) of degree n has property D(f) if it decomposes as a tensor product of a cyclic algebra of degree e=n/f containing L (the fixed subfield under σ e) and a cyclic subalgebra of degree f containing a f-th root of a. Although D(2) holds for every cyclic algebra of degree 4 and exponent 2, D(p) fails for Brauer algebras of degree p 2 and exponent p, and D(2) fails for Brauer algebras of degree 8 and exponent 2. Using this, one fills the gap in [6, Theorem 4] and [7, Theorem 7.3.28], to show that the example given there is indeed tensor indecomposable of degree p 2 and exponent p. An easy ultraproduct argument provides an example containing all p k roots of 1, for all k.

UR - http://www.scopus.com/inward/record.url?scp=4043111502&partnerID=8YFLogxK

U2 - 10.1007/BF02937323

DO - 10.1007/BF02937323

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AN - SCOPUS:4043111502

SN - 0021-2172

VL - 96

SP - 553

EP - 578

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -