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Content available remote Free monadic Tarski and MMI3-algebras
MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued Łukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI3-algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.
Content available remote Łukasiewicz residuation algebras with infimum
Łukasiewicz residuation algebras with an underlying ordered structure of meet semilattice (or iŁR-algebras) are studied. These algebras are the algebraic counter-part of the {->, lambda}-fragment of Łukasiewicz's many-valued logie. An equational basis for this class of algebras is shown. In addition, the subvariety of (n + 1)-valued iŁR-algebras for O < n < u is considered. In particular, the structure of the free finitely generated (n + 1)-valued iŁR-algebra is described. Moreover, a formuła to compute its cardinal number in terrns of n and the number of free generators is obtained.
Content available remote Free (n+1)-valued Łukasiewicz BCK-algebras
The cardinal of the finitely generated free (n + l)-valued Lukasiewicz BCK- algebras has been determined by different authors only for some values of n. In this article we find the formula that allows its calculus for every value of n. By the application of this formula for n = 1, n = 2, we corroborate the results obtained by L. Iturrioz and A. Monteiro (Rev. Un. Mat. Argentina, 22 (1966), 146) and L. Iturrioz and O.Rueda (Discrete Math., 18 (1977), 35-44). In addition we generalize the results found by A. V. Figallo (Rev. Un. Mat. Argentina, 41, 4 (2000), 33-43).
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