The lattice of convex subgroupoids of an ordered groupoid.
The lattice of solid -subgroups of a retractable group
The lattice of topologies of topological -groups
The Mitsch order on a semigroup.
The nil radical of an Archimedean partially ordered ring with positive squares
Let be an Archimedean partially ordered ring in which the square of every element is positive, and the set of all nilpotent elements of . It is shown that is the unique nil radical of , and that is locally nilpotent and even nilpotent with exponent at most when is 2-torsion-free. is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element is expressed as with positive ,...
The nonexistence of free complete vector lattices
The nonreduced order spectrum of a commutative ring.
The order topology for a von Neumann algebra
The order topology (resp. the sequential order topology ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part , the self-adjoint part of the unit ball , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other...
The orderability of completely regular semigroups.
The orderability of idempotent semigroups.
The orderability of idempotent semigroups
The orderability of regular semigroups.
The order-sum in classes of partially ordered algebras.
The partial-isometric crossed products of by the forward and backward shifts.
The principle of the largest terms and quantum large deviations
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
The quantifier semigroup for bipartite graphs.
The quasi-uniserial semigroups without zero, their arithmetics and their algebras.
The -free products of archimedean -groups
The objective of this paper is to give two descriptions of the -free products of archimedean -groups and to establish some properties for the -free products. Specifically, it is proved that -free products satisfy the weak subalgebra property.
The Redfield topology on some groups of continuous functions.
The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net implies that...
The restricted cancellation law in a Noether lattice