Direct factors of multilattice groups. II.
Subgroups of a directed distributive multilattice group are characterized which are direct factors of . The main result is formulated in Theorem 2.
Direct limits of cyclically ordered groups
Direct product decomposition of -algebras
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...
Direct product decompositions of directed groups
Direct product decompositions of pseudo effect algebras
Direct product factors in GMV-algebras
Direct summands and retract mappings of generalized -algebras
In the present paper we deal with generalized -algebras (-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of -algebras. The relations between -algebras and lattice ordered groups are essential for this investigation.
Directed convex subgroups of ordered groups
Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
Discrete ordered rings
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...
Distinguished completion of a direct product of lattice ordered groups
The distinguished completion of a lattice ordered group was investigated by Ball [1], [2], [3]. An analogous notion for -algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group is a direct product of lattice ordered groups
Distinguished extensions of an -algebra
Distributività rispetto all'unione e residuazione nei gruppoidi con ordine
Distributivität des -Untergruppenverbandes einer Verbandsgruppe
Distributivity in lattice ordered groups
Distributivity of intervals of torsion radicals
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 in certain automorphism groups
We study solvability of equations of the form in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.