engleski

Geometric Concepts in Some Special Classes of IM– Quasigroups

An idempotent medial quasigoup is a quasigroup which satisfies the identities of idempotency and mediality. Some geometric concepts can be introduced in each idempotent medial quasigroup. However, the definition of these concepts is given only in an implicit way. In some idempotent medial quasigroup with additional identities, these concepts could be defined in an explicit way. A number of geometric concepts in some special classes of idempotent medial quasigroups will be considered in this presentation. Specially, we are going to consider geometric concepts in a general GS–quasigroup and a quadratical quasigroup. We will study some simple geometric concepts whose existence will allow us to construct some more complicated geometric concepts. We will present the construction of an affine fullerene $C_{; ; 60}; ; $ in a general GS– quasigroup.

idempotent medial quasigroup ; affine fullerene ; GS–quasigroup ; quadratical quasigroup

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