Dual Effect Algebras And Horizontal Sums Of Sequential Effect Algebras

In this article, we first introduce the concept of effect algebras and sequence effect algebras. Secondly, dual effect algebras are introduced and some examples are given. Thirdly, we give some properties of the dual effect algebras and some relationships between effect algebras and dual effect algebras. Finally, some properties and horizontal sums of sequence effect algebras are discussed. Then, the structures of horizontal sums of two effect algebras and some properties are given. The article is divided into three chapters the main contents are organized as follows:The first chapter is an introduction of this paper. This chapter introduces the current research status of effect algebras and preparations, including the concepts of posets. bounds, effect algebras and sequence effect algebras. Subsequently, we give some basic properties of effect algebras and sequence effect algebras.The second chapter is devoted to dual effect algebras. In the first section, we introduce some history of effect algebras. In the second section, the definition of the dual effect algebra is given. Then we introduce several relevant typical examples of dual effect algebras. In the third section, we give five theorems about dual effect algebras in order to give some relationships between effect algebras and dual effect algebras.The third chapter is about some notes of sequence effect algebras and horizontal sums. In the first section, we introduce the present situation of the study about sequence effect algebras and horizontal sums. In the second section, we give two theorems about sequence effect algebras. In the third section, we introduce two effect algebras with a specific relationships-horizontal sum, and get some properties of the specific horizontal sums.