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An Algebraic Study of 2-generalized Łukasiewicz Algebras of Order n
C. Gallardo and A. Ziliani

In this paper a subvariety of m−generalized Łukasiewicz algebras of order n is investigated, particularly that one where m = 2. That is, L2n−algebras are the which ones verifying ƒ4x = x. Because 2 is the smallest number for which Lmn−algebras are not n-valued Łukasiewicz algebras and they constitute a particular case of BC K−algebras, here it is given the whole attention to them. First, some properties of atoms of L2n−algebras are shown, as they provide an important tool to give a complete description of subdirectly irreducible algebras. Next, finite algebras of this variety are studied and it is proved they are direct products of certain subalgebras determined by their atoms. Finally, free L2n−algebras with a finite set of free generators are described. Moreover, the particular cases n = 4 and n = 5 are developed in order to illustrate the applied method.

Keywords: m−generalized Łukasiewicz algebras of order n, Łukasiewicz algebras of order n, subdirectly irreducible algebras, free algebras.

MSC 2010: 03G10, 17C20, 08B20.

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