Commutative bounded integral residuated orthomodular lattices are Boolean algebras (Q432196)

\textit{M. Ward} and \textit{R. P. Dilworth} [Trans. Am. Math. Soc. 45, 335--354 (1939; Zbl 0021.10801)] proved that any complemented residuated lattice must be a Boolean algebra, which implies the claim of the title of the paper under review. The authors give another proof of this claim: Let \({\mathcal L}=(L,\vee,\wedge,',0,1)\) be an an orthomodular lattice. They derive their result (Theorem 2) with the aid of the following characterization (Theorem 1): \(\mathcal L\) is a Boolean algebra iff \(x\wedge y = x\wedge y'=0\) implies \(x=0\) for any \(x,y\in L\).