Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

[摘要] Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an ( o )-continuous state ω on E , which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

[关键词] ef fect algebra;state;modular lattice;finite element;compact element