### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-24 |

Number of pages | 24 |

Journal | arXiv.org e-Print archive |

Publication status | Published - 12 Jan 2017 |

### Fingerprint

### Keywords

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

### Cite this

*arXiv.org e-Print archive*, 1-24.

**Linearizing the Word Problem in (some) Free Fields.** / Schrempf, Konrad.

Research output: Contribution to journal › Article › Research

*arXiv.org e-Print archive*, pp. 1-24.

}

TY - JOUR

T1 - Linearizing the Word Problem in (some) Free Fields

AU - Schrempf, Konrad

N1 - 24 pages

PY - 2017/1/12

Y1 - 2017/1/12

N2 - 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.

AB - 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.

KW - math.RA

KW - 16K40, 03B25 (Primary), 16S10, 15A22 (Secondary)

KW - Wort-Problem

KW - Freier Schiefkörper

KW - Minimale Lineare Darstellung

KW - Linearisierung

KW - Rationale Folgen

KW - Realisierung

M3 - Article

SP - 1

EP - 24

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -