Linearizing the Word Problem in (some) Free Fields

Konrad Schrempf

Research output: Contribution to journalArticle


We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elements are given by minimal linear representations. It relies on the normal form of Cohn and Reutenauer and can be used more generally to (positively) test rational identities. Moreover we provide a construction of minimal linear representations for the inverse of non-zero elements.
Original languageEnglish
Pages (from-to)1-24
Number of pages24 e-Print archive
Publication statusPublished - 12 Jan 2017


  • math.RA
  • 16K40, 03B25 (Primary), 16S10, 15A22 (Secondary)


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