PreprintCC0arXiv
An explicit non-elementary matrix over a bivariate Laurent polynomial ring
Abstract
Let F be the fraction field of a discrete valuation ring. We give an explicit matrix in SL2(F[X±1,Y±1])∖ E2(F[X±1,Y±1]). The proof of non-elementarity is based on techniques developed by Peter Abramenko in his preprint arXiv:0808.1095v1.
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BibTeX
@misc{ionin2026explicit,
title = {{An explicit non-elementary matrix over a bivariate Laurent polynomial ring}},
author = {Vasiliy Ionin and Artem Semidetnov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04275},
eprint = {2609.04275},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04275},
note = {CC0},
}
RIS
TY - UNPB
TI - An explicit non-elementary matrix over a bivariate Laurent polynomial ring
AU - Vasiliy Ionin
AU - Artem Semidetnov
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.04275
UR - https://arxiv.org/abs/2609.04275
AB - Let F be the fraction field of a discrete valuation ring. We give an explicit matrix in SL_2(F[X^±1,Y^±1])∖ E_2(F[X^±1,Y^±1]). The proof of non-elementarity is based on techniques developed by Peter Abramenko in his preprint arXiv:0808.1095v1.
ER -