On certain classes of commutative \(g\)-dimonoids

Volodymyr Gavrylkiv, Inna Hlushak, Kateryna Koporkh, Natalia Mazurenko, Oksana Mykytsey

Abstract


We study \(g\)-dimonoids, which are algebraic structures equipped with two associative binary operations satisfying a prescribed system of axioms. We develop a construction of \(g\)-dimonoids based on inflations of semigroups, construct several new classes of \(2\)-dinilpotent commutative \(g\)-dimonoids, and investigate the isomorphism problem for these classes. As an application of these results, we obtain a structural description of all commutative \(g\)-dimonoids of order \(3\), up to isomorphism.


Keywords


semigroup, inflation of a semigroup, \(g\)-dimonoid, commutative \(g\)-dimonoid

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DOI: http://dx.doi.org/10.12958/adm2506

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