Decomposition of commutative ordered semigroups into archimedean components.
Demi-groupes 0-simples et complètement 0-simples totalement ordonnés. Application aux demi-groupes de matrices de Rees
Demi-groupes et catégories à involution
Die Verbände mit nichteinfacher Funktionenalgebra.
Direct decompositions of dually residuated lattice-ordered monoids
The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
Direct product decompositions of bounded commutative residuated -monoids
The notion of bounded commutative residuated -monoid (-monoid, in short) generalizes both the notions of -algebra and of -algebra. Let be a -monoid; we denote by the underlying lattice of . In the present paper we show that each direct...
Discussion of the structure of uninorms
The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing...
Distributività rispetto all'unione e residuazione nei gruppoidi con ordine
Distributivity of strong implications over conjunctive and disjunctive uninorms
This paper deals with implications defined from disjunctive uninorms by the expression where is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a -norm or a -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications...
Divisibility orders on semigroups. II.
DRl-semigroups and -algebras
Dually residuated -monoids having no non-trivial convex subalgebras
In this note we describe the structure of dually residuated -monoids (-monoids) that have no non-trivial convex subalgebras.