On closure operators on monoids
On colored set partitions of type B n
Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized and...
On completeness and direction in fuzzy relational systems.
The concepts of bounded subset, complete subset and directed subset, wich are well known in the context of partially ordered sets (X,≤), are extended in order to become appliable, with coherence, in fuzzy relational systems (X,R). The properties of these generalized structures are analyzed and operative exemples of them are presented.
On completion of cyclically ordered sets
On convexly isomorphic posets
On dense subsets of rational numbers
On determination of a cyclic order
On direct and subdirect product decompositions of partially ordered sets
On direct product decompositions of directed sets
On distances and metrics in discrete ordered sets
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the...
On distributive trices
A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.
On extended cyclic orders
On extensions of cyclic orders
On fixed edges of antitone self-mappings of complete lattices.
On fixed points of maximalizing mappings in posets.
On generalized derivations of partially ordered sets
Let be a poset and be a derivation on . In this research, the notion of generalized -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized -derivations are introduced. The properties of the fixed points based on the generalized -derivations are examined. The properties of ideals and operations related with generalized -derivations are studied.
On generating of relations
On ideals in De Morgan residuated lattices
In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal...
On incidence algebras and directed graphs.
On infinitely distributive ordered sets