The Research And Application Of The Cohesive Technique Of Homogeneous Effect Algebra

Effect algebras are important algebraic structures in quantum logic theory.Many scholars have studied its structures in different ways.Pasting is one of the important techniques in st.udying the structures of effect algebras.R.J.Greechie used the pasting techniques of Boolean algebras in the early stage to study the structires of orthomodular posets.Later,domestic and foreign scholars used it to study the structures of orthomodular posets,orthomodular lattices and lattice effect algebras.G.Jenca introduced homogeneous effect algebras in 2001.Homogeneous effect algebras include orthoalgebras,lattice effect algebras and effect algebras satisfying Riesz decomposition property.This thesis studies how to paste a homogeneous effect algebra with a family of effect algebras which sat.isfy the Riesz decomposition prop?erty.As an application of pasting techniques,then the relationships between Boolean algebras and RO algebras,Heyting algebras and other fuzzy logics are studied in this thesis.The main results are as follows:1.Some conditions for pasting a homogeneous effect algebra with a family of e:ffect algebras which satisfy the Riesz decomposition property are given.Thus the structures of homogeneous en1ect algebras are further characterized.2.The definition of Greechie diagrams of homogeneous effect algebras with-out atols of type of 2 is introduced.Then this thesis presents how to get a finite homogeneous effect algebra without atoms of type of 2 by replacing the atoms of an orthoalgebra with linear MV-effect,algebras.Thus the relationship between orthoal-gebras and homogeneous effect algebras is described.3.It is proved that any finite RO algebras can be obtained by replacing the atoms of Boolean algebras with linear R0 algebras in turn.And thus the relationship between Boolean algebras and RO algebras is characterized.Then the structures of Heyting algebras are studied in a similar way.A direct product decomposition theorem of Heyting algebras is given by using Boolean elements.And this thesis presents how to get a Heyting algebra by replacing the atoms of finite Boolean algebras with Heyting algebras.So the relationship between Boolean algebras and Heyting algebras is described.