On the pre-commutative envelopes of commutative algebras
We prove that every nilpotent commutative algebra over a field of characteristic zero can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a commutative algebra to have a pre-commutative envelope.
Authors
- P. S. Kolesnikov (ORCID: https://orcid.org/0000-0002-7534-1534)
- H. Alhussein (ORCID: https://orcid.org/0000-0002-8093-756X)
Institutions
- Novosibirsk State University (RU)
- Sobolev Institute of Mathematics (RU)
- Siberian State University of Telecommunications and Information Science (RU)
- Novosibirsk State University of Economics and Management (RU)
Publication Details
- Journal
- Journal of Algebra and Its Applications
- Published
- 2024-08-16
- DOI
- https://doi.org/10.1142/s0219498826500088
- Citations
- 1
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 1.27
Funders
- Russian Science Foundation