What question did this study set out to answer?

The aim is to establish conditions under which T-quasigroups with specific identities can be constructed.

February 17, 2026Open Access

On methods of constructing AD-quasigroups

Key Points

The aim is to establish conditions under which T-quasigroups with specific identities can be constructed.
Investigated T-quasigroups with AD and Schweitzer identities
Defined conditions for operations in T-quasigroup G
Utilized a special direct product of topological Abelian groups
Identified necessary and sufficient conditions for AD and Schweitzer identities
Created a new algebraic structure from G × G that follows specified laws
Demonstrated that the structure is non-associative while adhering to medial and semimedial laws

Abstract

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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Authors

Liubomir Chiriac

Natalia JOSU

Natalia Lupashco

Journals

SHILAP Revista de lepidopterología

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On methods of constructing AD-quasigroups

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Abstract

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