It is conjectured that a diagonal and degenerate 3\times 3 active--active component (i.e., lefthanded component) dominates in the effective 6\times 6 mass matrix for six Majorana neutrinos, three active and three (conventional) sterile, while its 3\times 3 active-sterile component (i.e., Dirac component) arises through a bimaximal-mixing unitary transformation from a structure  similar to the 3\times 3 mass matrices for charged leptons as well as up and down quarks. In such a texture, three neutrino masses are nearly degenerate, m₁ \simeq m₂ \simeq m₃ , though their mass-squared differences appear hierarchical, \Delta m²₂₁ \ll \Delta m²₃₂ \simeq \Delta m²₃₁, whereas the remaining three neutrino masses can be constructed to vanish, m₄ = m₅ = m₆ = 0 , or to be, as in Appendix A, degenerate in square with the previous masses, m₁ = |m₄|, m₂ = |m₅|, m₃ = |m₆|, in contrast to the familiar seesaw mechanism (in both cases). Appendices B and C are devoted to the author's idea of the algebraic compositeness of fundamental particles, resulting into three generations of Standard Model fermions and two generations of new bosons.

PACS numbers: 12.15.Ff, 14.60.Pq, 12.15.Hh