In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra $𝐀$ with constants $0,1$ is Boolean-like in case for all $a\in A$ the congruences $\theta \left(a,0\right)$ and $\theta \left(a,1\right)$ are complementary factor congruences of $𝐀$. We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue the investigation...

The paper deals with orthomodular lattices which are so-called horizontal sums of Boolean algebras. It is elementary that every such orthomodular lattice is simple and its blocks are just these Boolean algebras. Hence, the commutativity relation plays a key role and enables us to classify these orthomodular lattices. Moreover, this relation is closely related to the binary commutator which is a term function. Using the class $\mathscr{H}$ of horizontal sums of Boolean algebras, we establish an identity which...