On the dual space of an MS-algebra.
On the dynamics of (left) orderable groups
We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the case of braid...
On the embedding of ordered semigroups into ordered group
It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of -maher and -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered or -maher semigroup can be embedded into an ordered group.
On the extension of positive operators
On the extension of subadditive measures in lattice ordered groups
A lattice ordered group valued subadditive measure is extended from an algebra of subsets of a set to a -algebra.
On the ideal extensions in ordered semigroups.
On the Jakubík Problem on radical classes of lattice ordered groups
On the -valued categories of --ordered sets
The aim of this paper is to construct an -valued category whose objects are --ordered sets. To reach the goal, first, we construct a category whose objects are --ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an -valued category. Further we investigate the properties of this category, namely, we observe some special objects, special...
On the lattice group valued submeasures
On the lattice of semisimple classes of linearly ordered groups
On the lattice of torsion classes of lattice ordered groups
On the linear orderability of two classes of finite semigroups.
On the maximal Dedekind completion of a half partially ordered group
On the maximal Dedekind completion of a lattice ordered group
On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices
Let be a positive integer, and the set of all -circulant matrices over the Boolean algebra , . For any fixed -circulant matrix () in , we define an operation “” in as follows: for any in , where is the usual product of Boolean matrices. Then is a semigroup. We denote this semigroup by and call it the sandwich semigroup of generalized circulant...
On the multiplicative structure of a class of ordered semirings.
On the number of polynomials in ordered algebra
On the partial ordering of almost definite matrices
On the poset of tensor products on the unit interval
On the positivity of the unit element in a normed lattice ordered algebra