The first part of the paper deals with some subclasses of B-algebras and their applications to the semantics of SCI B , the Boolean strengthening of the sentential calculus with identity (SCI). In the second part a generalization of the McKinsey-Tarski construction of well-connected topological Boolean, algebras to the class of B-algebras is given.

This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.