Sequential convergences on pseudo MV-algebras
Sharp and fuzzy elements of an RC-group
Simple games in Łukasiewicz calculus and their cores
We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness...
Spectral topologies of dually residuated lattice-ordered monoids
Dually residuated lattice-ordered monoids (-monoids for short) generalize lattice-ordered groups and include for instance also -algebras (pseudo -algebras), a non-commutative extension of -algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.
State-homomorphisms on -algebras
Riečan [12] and Chovanec [1] investigated states in -algebras. Earlier, Riečan [11] had dealt with analogous ideas in -posets. In the monograph of Riečan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on -algebras. We remark that a different definition of a state in an -algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity...
States on basic algebras
States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain...
States on pseudo-effect algebras with general comparability
Strong subdirect products of MV-algebras
Subdirect product decompositions of -algebras
Subdirectly irreducible MV-algebras
In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.