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 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].