TY - JOUR

T1 - Independence of Quandle Axioms

AU - Borodin, A. N.

AU - Neshchadim, M. V.

AU - Simonov, A. A.

N1 - Borodin, A.N., Neshchadim, M.V. & Simonov, A.A. Independence of Quandle Axioms. Algebra Logic 64, 311–320 (2025). https://doi.org/10.1007/s10469-026-09836-2

PY - 2026/11

Y1 - 2026/11

N2 - We investigate the independence of axioms defining a quandle – an algebraic structure important in knot theory and combinatorial algebra. It is proved that all four axioms included in the standard definition of a quandle are independent. For finite quandles, one of the solvability axioms turns out to be a consequence of the others, owing to which it is possible to construct a minimal system of three axioms. An example of a right-distributive left quasigroup is constructed. As an application, for the constructed right-distributive systems, set-theoretic solutions to the Yang–Baxter equations and the corresponding associated groups are indicated.

AB - We investigate the independence of axioms defining a quandle – an algebraic structure important in knot theory and combinatorial algebra. It is proved that all four axioms included in the standard definition of a quandle are independent. For finite quandles, one of the solvability axioms turns out to be a consequence of the others, owing to which it is possible to construct a minimal system of three axioms. An example of a right-distributive left quasigroup is constructed. As an application, for the constructed right-distributive systems, set-theoretic solutions to the Yang–Baxter equations and the corresponding associated groups are indicated.

KW - Yang–Baxter equation axiom

KW - group

KW - quandle

KW - right quasigroup

UR - https://www.scopus.com/pages/publications/105045525942

UR - https://www.mendeley.com/catalogue/2fbedab8-0687-3395-b096-5ca4bfa805ab/

U2 - 10.1007/s10469-026-09836-2

DO - 10.1007/s10469-026-09836-2

M3 - Article

VL - 64

SP - 311

EP - 320

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -