@article { author = {Dvureˇcenskij, A. and Zahiri, O.}, title = {What are pseudo EMV-algebras?}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {1}, number = {1}, pages = {1-20}, year = {2020}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.29252/hatef.jahla.1.1.1}, abstract = {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]. }, keywords = {MV-algebra,EMV-algebra,pseudo EMV-algebra,maximal and normal ideal,statemorphism}, url = {https://jahla.hatef.ac.ir/article_101791.html}, eprint = {https://jahla.hatef.ac.ir/article_101791_8a912bffef18143a8fb5d9403ddd6d9f.pdf} }