<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> crossed products

Matzri, Eliyahu

doi:10.1016/j.jalgebra.2014.06.035

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…(5) Every algebra of degree 9 and exponent 9 over a field of characteristic different than 3 containing ρ 9 is similar to the product of 35840 symbol algebras of degree 9 and if it is of exponent 3 it is similar to the product of 277760 symbol algebras of degree 3. That is, len(9, 9) ≤ 35840 and len(9, 3) ≤ 277760 (Matzri [16]). ( 6) Every algebra of prime degree p over a field of characteristic different from p containing ρ p is similar to the tensor product of (p−1)!…”

Section: Known Results Results On Symbol Lengthmentioning

confidence: 99%

Symbol length in the Brauer group of a field

Matzri¹

2014

Preprint

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We bound the symbol length of elements in the Brauer group of a field K containing a C m field (for example any field containing an algebraically closed field or a finite field), and solve the local exponent-index problem for a C m field F . In particular, for a C m field F , we show that every F central simple algebra of exponent p t is similar to the tensor product of at most len(p t , F ) ≤ t(p m−1 − 1) symbol algebras of degree p t . We then use this bound on the symbol length to show that the index of such algebras is bounded by (p t ) (p m−1 −1) , which in turn gives a bound for any algebra of exponent n via the primary decomposition. Finally for a field K containing a C m field F , we show that every F central simple algebra of exponent p t and degree p s is similar to the tensor product of at most len(p t , p s , K) ≤ len(p t , L) symbol algebras of degree p t , where L is a C m+edL(A)+p s−t −1 field.

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Section: Known Results Results On Symbol Lengthmentioning

confidence: 99%

Symbol length in the Brauer group of a field

Matzri¹

2014

Preprint

Self Cite

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show abstract

“…5] for odd primes. For instance, when p = 3, it seems that the best result to date is that a central simple F -algebra which contains a maximal subfield L which is Galois over F with Gal(L/F ) ∼ = Z/3 × Z/3 (i.e., A is a Z/3 × Z/3-crossed product over F ) is similar to the tensor product of ≤ 31 symbol algebras of degree 3 over F [Mat14].…”

Section: Proof Of Case (2) Of the Main Theoremmentioning

confidence: 99%