Linearizing the Word Problem in (some) Free Fields
arXiv:1701.03378 · doi:10.1142/S0218196718500546
Abstract
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.
22 pages, slightly updated, accepted in IJAC
Cited by in corpus (4)
- Realizations of non-commutative rational functions around a matrix centre, I: synthesis, minimal realizations and evaluation on stably finite algebras
- Free Fractions: An Invitation to (applied) Free Fields
- A Factorization Theory for some Free Fields
- Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)