Abstract
We obtain a generalization of the ABC Theorem on locally nilpotent derivations to the case of the polynomials with \( m \) monomials such that each variable is included just in a sole monomial. As applications of this result we provide some construction of rigid and semirigid algebras and describe the Makar-Limanov invariant of algebras of a special form.
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Acknowledgment
The author is grateful to Sergey Gaifullin and to Ivan Arzhantsev for constant attention to this work.
Funding
The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics in 2023.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 5, pp. 1009–1022. https://doi.org/10.33048/smzh.2023.64.509
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Kikteva, V.V. Generalization of the ABC Theorem on Locally Nilpotent Derivations. Sib Math J 64, 1167–1178 (2023). https://doi.org/10.1134/S0037446623050099
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DOI: https://doi.org/10.1134/S0037446623050099