What are pseudo EMV-algebras?

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 nitely 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].