Decompositions for Relatively Normal Lattices

Join-semidistributive Lattices of Relatively Convex Sets

We give two sufficient conditions for the lattice Co(Rn, X) of relatively convex sets of Rn to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice can be embedded into Co(Rn, X), for a suitable finite subset X of Rn.

Representations of Relatively Complemented Modular Lattices

Introduction. A module over a ring will be said to be locally projective if and only if every finitely generated submodule is projective. As will be shown (7.14), it readily follows from known facts that if M is a locally projective module over a regular ring R, then the set L(M, R) of all finitely generated submodules of M is a relatively complemented modular lattice. This paper is concerned w...

Symmetric Chain Decompositions of Linear Lattices

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 Decompositions of Atomistic Algebraic Lattices