For a commutative semiring \( S \), by an \( S \)-algebra we mean a commutative semiring \( A \) equipped with a homomorphism \( S\to A \). We show that the subvariety of \( S \)-algebras determined by the identities \( 1+2x=1 \) and \( x^2=x \) is closed under non-empty colimits. The (known) closedness of the category of Boolean rings and of the category of distributive lattices under non-empty colimits in the category of commutative semirings both follow from this general statement.