The Relationship Among Several Algebraic Posets

In this dissertation,the concept of F-distributive posets is introduced,some of its properties are discussed,and the relationship between several classes of algebraic posets is studied.Firstly,it is proved that the poset P is F-distributive if and only if the family composed of cuts generated by all finite sets in P is also F-distributive;Then,the relationship between prealgebraic posets and Frink quasi algebraic posets is discussed.It is proved that the poset P is prealgebraic if and only if P is meet precontinuous and Frink quasialgebraic;Finally,the relationship between strongly algebraic poset and generalized strongly algebraic poset is discussed.It is proved that poset P is strongly algebraic if and only if P is prealgebraic and F-distributive if and only if P is strictly infinite distributive and generalized strongly algebraic.