Localization of MV-algebras
by
Busneag Dumitru
Professor, University of Craiova, Department of Mathematics, A.I.Cuza street,13, Ro-1100, Craiova, Romania
Coauthors: Piciu Dana

The concept of multiplier for distributive lattices was defined by W. H. Cornish in [7]. J. Schmid used the multipliers in order to give a non-standard construction of the maximal lattice of quotients for a distributive lattice (see [11]). A direct treatment of the lattices of quotients can be found in [12]. In [9], G. Georgescu exhibited the localisation lattice L_F of a distributive lattice L with respect to a topology F on L in a similar way as for rings (see [10]) or monoids (see [13]). For the case of Hilbert and Heyting algebras see [1]-[2] and respectively [8].

The concepts of MV - algebra of fractions relative to an /\ - closed system, MV - algebra of fractions and maximal MV - algebra of quotients was defined by the authors in [3]-[4].

The aim of the present work is to define the localisation MV - algebra of a MV- algebra A with respect to a topology F on A. Also, it is proved that the maximal MV - algebra of quotients (defined in [4]) and the MV - algebra of fractions relative to an /\ - closed system (defined in [3]) are MV - algebra of localization.

Keywords: MV - algebra, topology, F- multiplier, multiplier, MV - algebra of fractions, maximal MV - algebra of quotients, MV - algebra of localization.

AMS Subject Classification 2000: 06D35, 03G25.

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[3] D. Bu sneag, D. Piciu: MV-algebra of fractions relative to an /\ -closed system, Analele Universita tii din Craiova, Seria Matematica-Informatica, vol. XXX, (2003), 1-6

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Date received: February 26, 2003