A Note on 3×3-valued ?ukasiewicz Algebras with Negation

In 2004, C. Sanza, with the purpose of legitimizing study \(n\times m\)-valued ?ukasiewicz algebras negation (or \(\mathbf{NS}_{n\times m}\)-algebras) introduced \(3 \times 3\)-valued negation. Despite various results obtained about m}\)-algebras, structure free for this variety has not been determined yet. She only a bound their cardinal number finite generators. note we describe finitely generated \(NS_{3 3}\)-algebras and determine formula to calculate its in terms Moreover, obtain lattice \(\Lambda(\mathbf{NS}_{3\times 3})\) all subvarieties \(\mathbf{NS}_{3\times 3}\) show that varieties Boolean algebras, three-valued four-valued are proper 3}\).