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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.

Sameness between based universal algebras

Ricci G.

Demonstratio Mathematica

2009

Vol. 42, nr 1

3-22

This is the continuation of the paper "Transformations between Menger systems". To define when two universal algebras with bases "are the same", here we propose a universal notion of transformation that comes from a triple characterization concerning three representation facets: the determinations of the Menger system, analytic monoid and endomorphism representation corresponding to a basis. Hence, this notion consists of three equivalent definitions. It characterizes another technical variant and also the universal version of the very semi-linear transformations that were coordinate-free. Universal transformations allow us to check the actual invariance of general algebraic constructions, contrary to the seeming invariance of representation-free thinking. They propose a new interpretation of free algebras as superpositions of "analytic spaces" and deny that our algebras differ from vector spaces at fundamental stages. Contrary to present beliefs, even the foundation of abstract Linear Algebra turns out to be incomplete.

Łukasiewicz residuation algebras with infimum

Figallo A. V., Figallo A., Figallo M., Ziliani A.

Demonstratio Mathematica

2007

Vol. 40, nr 4

751-758

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.

Pojęcia niezależności w ujęciu algebraicznym - ogólny schemat Marczewskiego

Głazek K.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

1998

[Z] 34

31-48