Order completions of semiprime rings
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Order convergence and compactness
Order Convergence and Topological Completion of Commutative Lattice-Groups.
Order Maps And Unique Fixed Points In Complete Lattices
Order Preserving or Increasing Mappings Freedom or Incomparability Preserving Mappings
Order properties of splitting subspaces in an inner product space
Order relations on symmetric semigroups of transformations and on their homomorphic images.
Order theoretic variants of the fundamental theorem of compact semigroups.
Orderability of topological spaces by continuous preferences.
Ordered fields and the ultrafilter theorem
We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.
Ordered group invariants for one-dimensional spaces
We show that the Bruschlinsky group with the winding order is a homomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.
Ordered groups with greatest common divisors theory.
Ordered prime spectra of bounded -monoids
Ordered prime spectra of Boolean products of bounded -monoids are described by means of their decompositions to the prime spectra of the components.
Ordered semigroups characterized by their -fuzzy bi-ideals.
Ordered semigroups containing maximal elements.
Ordered semigroups containing minimal and maximal elements.
Ordered sets which support inverse semigroups : Three examples.
Ordered structures and projections.
Ordered topological spaces and the coproduct of bounded distributive lattices