Molecules of Post algebras (Q914712)

A non-zero element m of a poset P is called molecule if for all non-zero elements a,b\(\leq m\) of P there exists a nonzero lower bound of a, b in P. Molecules in Boolean algebras are atoms. A Post algebra is called molecular iff every element of P is the join of all molecules it contains. For a complete P it is shown that P is molecular iff P is isomorphic to a complete ring of sets.