Tensor products of division algebras and fields

Louis Rowen, David J. Saltman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This paper began as an investigation of the question of whether D1FD2 is a domain where the Di are division algebras and F is an algebraically closed field contained in their centers. We present an example where the answer is "no", and also study the Picard group and Brauer group properties of F1FF2 where the Fi are fields. Finally, as part of our example, we have results about division algebras and Brauer groups over curves. Specifically, we give a splitting criterion for certain Brauer group elements on the product of two curves over F.

Original languageEnglish
Pages (from-to)296-309
Number of pages14
JournalJournal of Algebra
Volume394
DOIs
StatePublished - 5 Nov 2013

Bibliographical note

Funding Information:
This work was supported by the U.S.–Israel BSF (grant no. 2010149 ).

Keywords

  • Brauer group
  • Division algebra
  • Picard group
  • Ramification
  • Schur index

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