%0 Journal Article %T What are pseudo EMV-algebras? %J Journal of Algebraic Hyperstructures and Logical Algebras %I University of Hatef (Hatef College University) %Z 2676-6000 %A Dvureˇcenskij, A. %A Zahiri, O. %D 2020 %\ 02/01/2020 %V 1 %N 1 %P 1-20 %! What are pseudo EMV-algebras? %K MV-algebra %K EMV-algebra %K pseudo EMV-algebra %K maximal and normal ideal %K statemorphism %R 10.29252/hatef.jahla.1.1.1 %X In the paper, we present EMV-algebras as a common generalization of MV-algebras and generalized Boolean algebras where a top element is not assumed a priori. In addition, we present a non-commutative generalization of EMV-algebras, pseudo MV-algebras and of generalized Boolean algebras. We present main representation results showing a very close connection of pseudo EMValgebra with pseudo MV-algebras, and we give a categorical representation of the category o pseudo EMValgebras without top element. We study also states as analogs of finitely additive states, their topological properties, and we present an integral representation of states by σ-additive probability measures. The paper is a survey over papers [13]{[19]. %U https://jahla.hatef.ac.ir/article_101791_8a912bffef18143a8fb5d9403ddd6d9f.pdf