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.
Representing Upper Probability Measures over Rational Lukasiewicz Logic.
Riemann average truth-value of Łukasiewicz formulas