  The Z2 topological invariant is defined in the chiral d-wave superconductor
having a triangular lattice in the presence of the 120 degrees magnetic
ordering. By analyzing the Z2 invariant, we determine the conditions of
implementing nontrivial phases in the model with regard to superconducting
pairings between nearest and next nearest neighbors. It is often supposed in
such system that the pairing parameter between nearest neighbors should be
equal to zero due to influence of the intersite Coulomb interaction. We show
that taking into account even weak pairings in the first coordination sphere
leads to the disappearance of the gapless excitations of the bulk spectrum in
the wide region of the parameter space. Thus topological invariants can be
defined in such region. Solving the problem of open edges it is shown that the
zero energy modes are realized basically in the topologically nontrivial
phases. Such zero modes are topologically protected Majorana modes. A
connection between the Z2 invariant calculated at the symmetric points of the
Brillouin zone with respect to the electron-hole symmetry and the integer
topological invariant of the ground state of the 2D lattice expressed in terms
of the Green functions is established in the presence of noncollinear magnetic
ordering.
