Some closure properties in monoids.
Some comments and examples on generation of (hyper-)archimedean -groups and -rings
This paper systematizes some theory concerning the generation of -groups and reduced -rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an -group, or an identity to an -ring and find significant contrasts between these cases. In -groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by...
Some examples of hyperarchimedean lattice-ordered groups
All ℓ-groups shall be abelian. An a-extension of an ℓ-group is an extension preserving the lattice of ideals; an ℓ-group with no proper a-extension is called a-closed. A hyperarchimedean ℓ-group is one for which each quotient is archimedean. This paper examines hyperarchimedean ℓ-groups with unit and their a-extensions by means of the Yosida representation, focussing on several previously open problems. Paul Conrad asked in 1965: If G is a-closed and M is an ideal, is G/M a-closed? And in 1972:...
Some ideas for comparison of Bellman chains
In this paper we are exploiting some similarities between Markov and Bellman processes and we introduce the main concepts of the paper: comparison of performance measures, and monotonicity of Bellman chains. These concepts are used to establish the main result of this paper dealing with comparison of Bellman chains.
Some properties of an archimedean -group
Some properties of lattice ordered Rees matrix semigroups
Some properties of Lorenzen ideal systems
Let be a partially ordered abelian group (-group). The construction of the Lorenzen ideal -system in is investigated and the functorial properties of this construction with respect to the semigroup of all -ideal systems defined on are derived, where for and a lower bounded subset , . It is proved that Lorenzen construction is the natural transformation between two functors from the category of -groups with special morphisms into the category of abelian ordered semigroups.
Some properties of residuated lattices
We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.
Some remarks on certain partially ordered semigroups.
Some remarks on Lorenzen -group of partly ordered groups
Some Remarks or v-Ideal Systems and Categories of semigroups
Some results in bipolar-valued fuzzy ordered AG-groupoids
In this paper, we introduce the concept of bipolar-valued fuzzification of ordered 𝓐𝓖-groupoids and discuss some structural properties of bipolar-valued fuzzy two-sided ideals of an intra-regular ordered 𝓐𝓖-groupoid.
Some results on ordered filters of implicative semigroups.
Some results on the weak dominance relation between ordered weighted averaging operators and T-norms
Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More...
Sous-demi-groupes convexes des demi-groupes totalement ordonnés. Erratum et compléments
Sous-demi-groupes convexes des demi-groupes totalement ordonnés
Sous-groupes et groupes quotients d'un groupe préordonné
Spaces of Vector-Valued Measurable Functions.
Spaces whose connected expansion preserve connected subsets
Spaces in which all prime -ideals of are minimal or maximal
Quasi -spaces are defined to be those Tychonoff spaces such that each prime -ideal of is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of -spaces. The compact quasi -spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi -spaces is given. If is a cozero-complemented space and every nowhere dense zeroset...