Answers are grounded in this paper and cite their sources.
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.
No takes yet. Share an insight, caveat, or question.
Alhussein et al. (2024) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: