Hedl\'\i kov\'a, J., Relatively orthomodular lattices, Discrete
Mathematics.

 M.F. Janowitz defined a generalized orthomodular lattice
[GOM--lattice, GOML] as a lattice with a smallest element $0$ and
with an orthogonality relation $\perp$. He proved that any such a
lattice is isomorphic to a prime ideal of an orthomodular lattice
[OM--lattice, OML]. Equivalently, a GOM--lattice can be defined as a
lattice with a smallest element $0$, in which every interval
containing $0$ is an OM--lattice and a natural additional condition
is satisfied.

  We define a relatively orthomodular lattice [ROM--lattice, ROML]
as a lattice with a commutativity relation $C$, in such a way that
every GOM--lattice is an ROM--lattice. Equivalently, an ROM--lattice
can be defined as a lattice in which every interval is an
OM--lattice and a natural additional condition is satisfied. We
prove that every ROM--lattice is isomorphic to a prime dual ideal of
a GOM--lattice and that this embedding is in some sense minimal.
Consequently, an ROM--lattice can be defined as a sublattice of an
OM--lattice closed under the relative orthocomplements.
