Modular and Distributive Equalities in Lattices
Modular and metric multilattices
Modular atomic effect algebras and the existence of subadditive states
Lattice effect algebras generalize orthomodular lattices and -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
Modular, distributive and simple intervals of the lattice of topologies
Modular elements in congruence lattices of -sets.
Modular functions on multilattices
We prove that every modular function on a multilattice with values in a topological Abelian group generates a uniformity on which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of .
Modular median algebras
Modular ordered sets
Modular posets and semigroups.
Modular Substructures in Pseudomodular Lattices.
Modulare Inzidenzstrukturen
Modulare Polynomverbände über endlichen distributiven Verbänden.
Modularité et distributivité affaibliés dans les lattis
Modularity and distributivity of the lattice of -closed subsets of an algebraic structure
Let be an algebraic structure of type and a set of open formulas of the first order language . The set of all subsets of closed under forms the so called lattice of -closed subsets of . We prove various sufficient conditions under which the lattice is modular or distributive.
Modularity and distributivity of tolerance lattices of commutative inverse semigroups
Modularity and distributivity of tolerance lattices of commutative separative semigroups
Modularity, atomicity and states in Archimedean lattice effect algebras.
Modularity in generalized orthomodular lattices
Modules ordonnés injectifs
Modus ponens on Boolean algebras revisited.
In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.