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Free monadic Tarski and MMI3-algebras

Entizne R. V., Monteiro L. F., Savini S. M., Viglizzo I. D.

Demonstratio Mathematica

2014

Vol. 47, nr 3

509--521

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.

Endomorphisms of implication algebras

Gaitán H.

Demonstratio Mathematica

2014

Vol. 47, nr 2

284--288

In this note we prove that if two implication algebras have isomorphic monoids of endomorphisms then they are isomorphic.