Frobenius type theorems in the noncommutative case

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Abstract

The classification of semilinear transformations preserving the determinant over a noncommutative local ring is given. For local Ore domains we obtain a classification of Adjamagbo determinant preservers. The developed technique allows us to classify Dieudonné determinant preservers for division rings which may be infinite dimensional over the center.

Original languageEnglish
Pages (from-to)293-311
Number of pages19
JournalLinear and Multilinear Algebra
Volume48
Issue number4
DOIs
StatePublished - 2001
Externally publishedYes

Bibliographical note

Funding Information:
*This work is partially supported by RFBR Grants NN 96-15-96050, 99-01-00382. +,-mail: [email protected]

Keywords

  • Dieudonné determinant
  • Linear preservers
  • Local rings

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