Z3×Z3 crossed products: Journal of Algebra

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Abstract

Let A be the generic abelian crossed product with respect to Z3×Z3. In this note we show that A is similar to the tensor product of 4 symbol algebras (3 of degree 9 and one of degree 3) and if A is of exponent 3 it is similar to the product of 31 symbol algebras of degree 3. We then use [9] to prove that if A is any algebra of degree 9 then A is similar to the product of 35. 840 symbol algebras (8960 of degree 3 and 26. 880 of degree 9) and if A is of exponent 3 it is similar to the product of 277. 760 symbol algebras of degree 3. We then show that the essential 3-dimension of the class of A is at most 6. © 2014 Elsevier Inc.
Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalJournal of Algebra
Volume418
DOIs
StatePublished - 1 Nov 2014

Bibliographical note

Cited By :2

Export Date: 23 March 2022

CODEN: JALGA

Correspondence Address: Matzri, E.

Funding details: United States-Israel Binational Science Foundation, BSF, 2010149

Funding text 1: This work was supported by the United States-Israel Binational Science Foundation (Grant No. 2010149 ).

Keywords

  • Abelian crossed products
  • Brauer group
  • Division algebras

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