On weak direct product decompositions of lattices and graphs

Direct Product Decompositions of Lattices , Closures andRelation

In this paper we study the direct product decompositions of closure operations and lattices of closed sets. We characterize the direct product decompositions of lattices of closed sets in terms of closure operations, and nd those decompositions of lattices which correspond to the decompositions of closures. If a closure on a nite set is represented by its implication base (i.e. a binary relatio...

Direct Product Decompositions of Infinitely Distributive Lattices

Let α be an infinite cardinal. Let Tα be the class of all lattices which are conditionally α-complete and infinitely distributive. We denote by T ′ σ the class of all lattices X such that X is infinitely distributive, σ-complete and has the least element. In this paper we deal with direct factors of lattices belonging to Tα. As an application, we prove a result of Cantor-Bernstein type for latt...

Direct product decompositions of lattices, closures and relation schemes

In this paper we study direct product decompositions of closure operations and lattices of closed sets. We characterize direct product decompositions of lattices of closed sets in terms of closure operations, and find those decompositions of lattices which correspond to the decompositions of closures. If a closure on a finite set is represented by its implication base (i.e. a binary relation on...

Direct Decompositions of Atomistic Algebraic Lattices

Decompositions of Banach Lattices into Direct Sums

We consider the problem of decomposing a Banach lattice Z as a direct sum Z = X @ Y where X and Y are complemented subspaces satisfying a condition of incomparability (e.g. every operator from Y to X is strictly singular). We treat both the atomic and nonatomic cases. In particular we answer a question of Wojtaszczyk by showing that L1 fflL2 has unique structure as a nonatomic Banach lattice. O...