## Abstract

We show that there is no nontrivial group homomorphism En(R) → E_{n-1}(R) over commutative local rings and division rings for n ≥ 3, respectively. It gives a negative answer to Ye's problem (see [S. K. Ye, Low-dimensional representations of matrix group actions on CAT(0) spaces and manifolds, J. Algebra 409 (2014) 219-243]) for the above rings.

Original language | English |
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Article number | 17500104 |

Journal | Journal of Algebra and its Applications |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

## Keywords

- Elementary group
- division ring
- homomorphism
- local ring

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