New operations on orthomodular lattices: ``Disjunction'' and ``conjunction'' induced by Mackey decompositions (Q698543)

The author studies new conjuction and disjunction operations on orthomodular lattices. These operations are sharp and flat ones, and they are connected with a so-called Mackey decomposition of two elements. On Boolean algebras, or on compatible elements, they coincide. These operations are not necessarily associative; they are only on Boolean algebras. The author also studies an order connected with flat and sharp operations, and finally he gives some properties connected with states.