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 nonzero elements.
| Original language | English |
|---|---|
| Pages (from-to) | 1209-1230 |
| Number of pages | 22 |
| Journal | International Journal of Algebra and Computation |
| Volume | 28 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 1 Nov 2018 |
Keywords
- word problem
- minimal linear representation
- linearization
- realization
- admissible linear system
- rational series
- Word problem