Kybernetika 45 no. 6, 1040-1051, 2009

Atomicity of Lattice Effect Algebras and Their Sub-Lattice Effect Algebras

Jan Paseka and Zdenka Riečanová


We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology.


MV-algebras, non-classical logics, effect algebras, D-posets, atomicity


03G12, 06D35, 06F25, 81P10