Abstract
AbstractThe article aims at describing finitely generated free algebras in certain finitely generated varieties of commutative BCK-algebras. To achieve this, we first investigate homomorphisms from free commutative BCK-algebras to free ŁBCK-algebras that extend the insertion of generators. The approach allows us to utilize existing results on free ŁBCK-algebras. The second step involves valuations and their equivalence. An essential part is to count the number of non-equivalent valuations with specific properties. With the number in hand, we can provide a comprehensive description of the free algebras.
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