TY - JOUR

T1 - Constructions of Quandles over Groups, Modules, and Near-Rings

AU - Borodin, A. N.

AU - Neshchadim, M. V.

AU - Simonov, A. A.

N1 - Borodin, A.N., Neshchadim, M.V. & Simonov, A.A. Constructions of Quandles over Groups, Modules, and Near-Rings. Sib Math J 67, 18–27 (2026). https://doi.org/10.1134/S0037446626010039 The work was supported by the Fundamental Research Program of the Siberian Branch of the Russian Academy of Sciences (no. I.1.5, Project FWNF–2026–0029).

PY - 2026/1

Y1 - 2026/1

N2 - Various constructions of generalized Alexander quandles are studied.It is proved that, up to isomorphism, they reduce to two types.Conditions are found under which such quandles are abelian.A construction of an extension of a generalized Alexander quandle to the direct product of two groups is given.Conditions for constructing a quandle over a module and a near-ring are found.

AB - Various constructions of generalized Alexander quandles are studied.It is proved that, up to isomorphism, they reduce to two types.Conditions are found under which such quandles are abelian.A construction of an extension of a generalized Alexander quandle to the direct product of two groups is given.Conditions for constructing a quandle over a module and a near-ring are found.

KW - 512.548+515.162.8

KW - antiautomorphism

KW - automorphism

KW - distributivity

KW - generalized Alexander quandle

KW - group

KW - module

KW - near-ring

KW - quandle

KW - ring

UR - https://www.scopus.com/pages/publications/105028895287

UR - https://www.mendeley.com/catalogue/429b90ce-26cc-333b-bad4-558f9a200abc/

U2 - 10.1134/S0037446626010039

DO - 10.1134/S0037446626010039

M3 - Article

VL - 67

SP - 18

EP - 27

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

M1 - 3

ER -