PreprintCC BY 4.0arXiv
The finite basis problem for varieties modulo x^3=0
Abstract
We prove that any variety of associative algebras over a Noetherian commutative ring with unity satisfying the identity x^3=0 is finitely based. This property has been known for the varieties satisfying the identity x^2=0. On the other hand, there are varieties satisfying the identity x^6=0 that are not finitely based.
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BibTeX
@misc{kireeva2026finite,
title = {{The finite basis problem for varieties modulo x^3=0}},
author = {Elena Kireeva and Alexei Krasilnikov and Vladimir Shchigolev},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03923},
eprint = {2611.03923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03923},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The finite basis problem for varieties modulo x^3=0
AU - Elena Kireeva
AU - Alexei Krasilnikov
AU - Vladimir Shchigolev
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03923
UR - https://arxiv.org/abs/2611.03923
AB - We prove that any variety of associative algebras over a Noetherian commutative ring with unity satisfying the identity x^3=0 is finitely based. This property has been known for the varieties satisfying the identity x^2=0. On the other hand, there are varieties satisfying the identity x^6=0 that are not finitely based.
ER -