We research T-quasigroups with AD identity and Schweitzer identity. The necessary and sufficient condition has been determined that in the T-quasigroup G of the form x • y=ϕ(x)+ψ(y), AD identity and the Schweitzer identity are true. We have used the concept of a special direct product of an topological Abelian group G and proved that a binary operation can be defined on the set G × G, such that the new algebraic structure is a non-associative topological quasigroups obeying medial, semimedial and AD laws.
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Liubomir Chiriac
Natalia JOSU
Natalia Lupashco
SHILAP Revista de lepidopterología
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Chiriac et al. (Thu,) studied this question.
www.synapsesocial.com/papers/6994055d4e9c9e835dfd644e — DOI: https://doi.org/10.36120/2587-3644.v20i2.128-139