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

Key Points

• Generalized Alexander quandles reduce to two types up to isomorphism, highlighting their structural diversity,
• Key conditions have been determined for when these quandles can be classified as abelian, facilitating their study,
• A method for extending a generalized Alexander quandle to the direct product of two groups is provided, enriching potential applications,
• This work suggests deeper insights into algebraic structures, calling for further exploration of modules and near-rings.

Abstract