  Neutrino masses and mixings are analyzed in terms of left-handed fields and a
6x6 complex symmetric mass matrix whose singular values are the neutrino
masses. An angle x_nu characterizes the kind of the neutrinos, with x_nu = 0
for Dirac neutrinos and x_nu = pi/2 for Majorana neutrinos. If x_nu = 0, then
baryon-minus-lepton number is conserved. When x_nu is approximately zero, the
six neutrino masses coalesce into three nearly degenerate pairs. Thus the
smallness of the differences in neutrino masses exhibited in the solar and
atmospheric neutrino experiments and the stringent limits on neutrinoless
double beta decay are naturally explained if B-L is approximately conserved and
neutrinos are nearly Dirac fermions. If one sets sin(x_nu) = 0.003, suppresses
inter-generational mixing, and imposes a quark-like mass hierarchy, then one
may fit the essential features of the solar, reactor, and atmospheric neutrino
experiments with otherwise random mass matrices in the eV range.
  This B-L model leads to these predictions: neutrinos oscillate mainly between
flavor eigenfields and sterile eigenfields, and so the probabilities of the
appearance of neutrinos or antineutrinos are very small; neutrinos may well be
of cosmological importance; in principle the disappearance of the tau neutrino
should be observable; and neutrinoless double beta decay is suppressed by an
extra factor of < 10^(-5) and hence will not be seen in the Heidelberg/Moscow,
IGEX, GENIUS, or CUORE experiments.
