On some properties of submeasures on MV-algebras
On some types of radical classes
Let be an infinite cardinal. We denote by the collection of all -representable Boolean algebras. Further, let be the collection of all generalized Boolean algebras such that for each , the interval of belongs to . In this paper we prove that is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized -algebras.
On the extension of -poset valued measures
A variant of Alexandrov theorem is proved stating that a compact, subadditive -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.
On the -completeness of pseudo MV-algebras
On varieties of pseudo -algebras
In this paper we investigate the relation between the lattice of varieties of pseudo -algebras and the lattice of varieties of lattice ordered groups.
Open problems posed at the eighth international conference on fuzzy set theory and applications
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Operators on -algebras
Closure -algebras are introduced as a commutative generalization of closure -algebras, which were studied as a natural generalization of topological Boolean algebras.
Polars and annihilators in representable -monoids and -algebras
Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras
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.
Prime ideals and polars in DR-monoids and BL-algebras
Projectability and weak homogeneity of pseudo effect algebras
In this paper we deal with a pseudo effect algebra possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, can be represented as an interval of a unital partially ordered group . We prove that is projectable (strongly projectable) if and only if is projectable (strongly projectable). An analogous result concerning weak homogeneity of and of is shown to be valid.
Pseudo -algebras and -monoids
It is shown that pseudo -algebras are categorically equivalent to certain bounded -monoids. Using this result, we obtain some properties of pseudo -algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo -algebras and, in conclusion, we prove that they form a variety.
Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients
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...
Quasivarieties of pseudo-MV-algebras.
Radical classes of -algebras
Radicals and complete distributivity in relatively normal lattices
Lattices in the class of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity of algebraic...
Radicals in non-commutative generalizations of MV-algebras
Regular representations of semisimple MV-algebras by continuous real functions
Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras
In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) Gödel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a Gödel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.
Remarks on pseudo MV-algebras
Pseudo MV-algebras (see e.g., [4, 6, 8]) are non-commutative extension of MV-algebras. We show that every pseudo MV-algebra is isomorphic to the algebra of action functions where the binary operation is function composition, zero is x ∧ y and unit is x. Then we define the so-called difference functions in pseudo MV-algebras and show how a pseudo MV-algebra can be reconstructed by them.