PreprintarXiv licencearXiv
New results on nil rings
Abstract
For every field~Bbbk, we construct a non-nilpotent nil algebra~A whose Lie algebra A(−) is generated by ten elements. For Bbbk = ℤp, its adjoint group can also be generated by ten elements. Moreover, for every field Bbbk algebraic over its prime subfield, we construct a finitely presented algebra B over Bbbk whose Jacobson radical is not nil. These results were found with the assistance of Aristotle (Harmonic).
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BibTeX
@misc{gubarev2026results,
title = {{New results on nil rings}},
author = {Vsevolod Gubarev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34463},
eprint = {2610.34463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34463},
}
RIS
TY - UNPB
TI - New results on nil rings
AU - Vsevolod Gubarev
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34463
UR - https://arxiv.org/abs/2610.34463
AB - For every field~Bbbk, we construct a non-nilpotent nil algebra~A whose Lie algebra A^(−) is generated by ten elements. For Bbbk = ℤ_p, its adjoint group can also be generated by ten elements. Moreover, for every field Bbbk algebraic over its prime subfield, we construct a finitely presented algebra B over Bbbk whose Jacobson radical is not nil. These results were found with the assistance of Aristotle (Harmonic).
ER -