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math.RA2026
Idempotents and Powers of Ideals in Quandle Rings
Valeriy Bardakov, Mohamed Elhamdadi
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a sem…
math.RA2025
Self-distributive algebras and bialgebras
Valeriy G. Bardakov, Tatiana A. Kozlovskaya, Dmitry V. Talalaev
This article is devoted to the study of self-distributive algebraic structures: algebras, bialgebras; additional structures on them, relations of these structures with Hopf algebra…
math.RA2024
Algebra, group, and Hopf Rota-Baxter operators
Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin
We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to def…