Skip to content
DraconiticResearch
Search Sources API
182,549 studies31 sourcesUpdated 52 min ago
PreprintCC0arXiv

The Parafree Conjecture for Lie rings and associative algebras

  • Vasily Ionin
  • Roman Mikhailov
Open at sourcePDFDOICite

Abstract

We construct a finitely generated parafree Lie ring with nonzero second homology and, over every nonzero commutative ring, a finitely generated parafree augmented associative algebra with nonzero second homology. These examples disprove the analogues of the Parafree Conjecture for Lie rings and for augmented associative algebras. Our constructions also provide finitely generated parafree examples that are not finitely presented, both in the Lie-ring and augmented-algebra settings.

Related

  1. The Hilbert Basis Theorem for Non-Associative Skew Power Series Rings and Non-Associative Skew Laurent Series Rings over a Non-Associative Coefficient Ring
    Darwin P. Mangubat, Jocelyn P. Vilela, Johan Richter
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. A Non-linearizable Action of S3 on Free Metabelian Lie and Associative Algebras
    Altyngul Naurazbekova, Ualbai Umirbaev
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Varieties of associative algebras with quadratic codimension growth
    Wesley Quaresma Cota, Luiz Henrique de Souza Matos, Pedro Quintino
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Derived Associative Algebras and Cyclic Cohomology of Q-manifolds
    Andrew James Bruce
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  5. Anti-quadratic nearly associative algebras
    Sofiane Bouarroudj, Hamza El Ouali
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{ionin2026parafree,
  title = {{The Parafree Conjecture for Lie rings and associative algebras}},
  author = {Vasily Ionin and Roman Mikhailov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.20570},
  eprint = {2608.20570},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.20570},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - The Parafree Conjecture for Lie rings and associative algebras
AU  - Vasily Ionin
AU  - Roman Mikhailov
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2608.20570
UR  - https://arxiv.org/abs/2608.20570
AB  - We construct a finitely generated parafree Lie ring with nonzero second homology and, over every nonzero commutative ring, a finitely generated parafree augmented associative algebra with nonzero second homology. These examples disprove the analogues of the Parafree Conjecture for Lie rings and for augmented associative algebras. Our constructions also provide finitely generated parafree examples that are not finitely presented, both in the Lie-ring and augmented-algebra settings.
ER  -