Localization of m–generalized Łukasiewicz Algebras of Order n
C. Gallardo and A. Ziliani
In 2001, m–generalized Łukasiewicz algebras of order n (or Lmn– algebras) were introduced by J. Vaz de Carvalho and T. Almada as a generalization of Łukasiewicz algebras of order n and a particular case of Ockham algebras. In this article the localization on Lmn– algebras is developed. More precisely, the Lmn– algebra of fractions relative to a ∧–closed system is obtained. Besides, the concept of F–multiplier where F is a topology on an Lmn– algebra L is defined and it is proved that the Lmn– algebra of fractions L[C] associated with an ∧–closed system C of L is isomorphic to the localization Lmn– algebra LFC with respect to the topology FC associated to C. Finally, the notion of Lmn– algebra of quotients is considered and the existence of a maximal quotients Lmn– algebra is shown.
Keywords: m–generalized Łukasiewicz algebra of order n, ∧–closed system, multiplier, localization algebra, algebra of fractions, maximal algebra of quotients.
MSC (2010): 06D30, 03G20.