  In the canonical seesaw mechanism of neutrino mass, lepton number is only
multiplicatively conserved, which enables the important phenomenon of
leptogenesis to occur, as an attractive explanation of the present baryon
asymmetry of the Universe. A parallel possibility, hitherto unrecognized, also
holds for baryon number and baryogenesis. This new idea is shown to be
naturally realized in the context of a known supersymmetric string-inspired
extension of the Standard Model, based on E(6) particle content, and having an
extra U(1)_N gauge symmetry. Within this framework, two-loop radiative neutrino
masses are also possible, together with a new form of very long-lived matter.
