reducible m-ideals in banach spaces

For an arbitrary nontrivial m-ideal j in a banach space x, is there a m-ideal k inx such that j ∩ k is reducible? to answer this question, we look for conditions under whichthe setr_j −m(x) := {k ∈ n −m − ideal(x) : j ∩ k ∈ r −m − ideal(x)}is nonempty, where m − ideal(x) and r −m − ideal(x) denote the set of of m-ideals and reducible m-ideals in x, respectively. further, some important properties on r_j −m(x) are established.