The embedding of an ordered semigroup into an le-semigroup.
The epis of the category of ordered algebras and -continuous homomorphisms
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The essential cover and the absolute cover of a schematic space
A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...
The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks
Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...
The functional equation f(xy) = ff(x) xy ff(y) in a partially ordered monoid.
The Galois connection between weak torsion and sub-product classes of -groups
The globals of pseudovarieties of ordered semigroups containing and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.
The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin
Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.
The graphs of join-semilattices and the shape of congruence lattices of particle lattices
We attach to each -semilattice a graph whose vertices are join-irreducible elements of and whose edges correspond to the reflexive dependency relation. We study properties of the graph both when is a join-semilattice and when it is a lattice. We call a -semilattice particle provided that the set of its join-irreducible elements satisfies DCC and join-generates . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...
The group of divisibility of
The -Classes of Archimedean -groups with Weak Unit
denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar and from universal algebra are here meant in . and denote the integers and the reals, with unit 1, qua-objects. denotes a non-void finite set of positive integers. Let be non-void and not . We show(1), and(2) if and only if Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted...
The hulls of semiprime rings
The ideal and new interval topologies on l-groups
The Ideal extensions of ordered semigroups
The injective hull of an archimedean f-algebra
The intersection graph of a simply ordered semigroup.
The intersection graph on an ordered commutative semigroup.
The Interval Topology of an -Group
The inverse semigroup of a sumordered semiring.