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Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

100%

Piciu D.

Open Mathematics

2004

tom 2

nr 2

199-217

The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

84%

Cabrer L., Celani S.

Open Mathematics

2006

tom 4

nr 4

600-623

In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.

Ograniczanie wyników

2 Open Mathematics

1 Cabrer L.

1 Celani S.

1 Piciu D.

1 2006

1 2004

Wyniki wyszukiwania

Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras