Linearizing the word problem in (some) free fields

Konrad Schrempf

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 nonzero elements.
Original languageEnglish
Pages (from-to)1209-1230
Number of pages22
JournalInternational Journal of Algebra and Computation
Issue number7
Publication statusPublished - 1 Nov 2018


  • word problem
  • minimal linear representation
  • linearization
  • realization
  • admissible linear system
  • rational series
  • Word problem


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