Considering top element of Boolean algebras optional, Stone extended their class to “generalized Boolean algebras” (GBAs), and initiated their research by methods of abstract algebra, but also stated that his treatment of these structures is not the “most natural”. Attributing his dissatisfaction to the treatment of GBAs as “double composition systems”, these are presented here as commutative monoids with invertible operations, though in contrast with groups, not uniquely invertible. This treatment as “single composition systems” turn GBAs into “algebras of measurable objects” suggesting their extensive use in measure theory.