Rare Z0 decays as a probe of supersymmetric models with explicitly broken R-parity

We consider a minimal multiplet supersymmetric extension of the standard model in which SU(3)xSU(2)LxU(1)Y invariant Yukawa interactions break R-parity and violate lepton or baryon number. We calculate the branching ratio for Z0 decay to single sparticle channels and identify new signals which could arise as a consequence of R-parity breaking. For the theoretically favoured case in which the LSP is a neutralino, we find that there are three possible signals which cannot be produced by standard model physics, and would therefore be a signature of R-parity broken supersymmetry. We calculate the event rate to be expected for such 'exotic' signals at present and future e+e- and pp colliders. The event rates which we have obtained rule out the possibility of discovery at LEP(I), and observation of R-parity breaking in Z0 decay may only be possible at high luminosity machines such as the LHC and SSC. (orig.)