The fluctuation conductivity above ${\mathit{T}}_{\mathit{c}}$ was measured in (Bi,Pb)-Sr-Ca-(${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$,${\mathrm{Ni}}_{\mathit{x}}$)-O superconductors having the 110-K phase. The temperature dependence of the paraconductivity can be described by a power law following Aslamazov-Larkin theory. For nondoped (x=0) samples, the conductivity data show a two-dimensional fluctuation of the order parameter, whereas Ni-doped samples show lower-dimensional fluctuations and reduced widths of the resistive transition. The critical exponent of the power law and its amplitude are well correlated with ${\mathit{T}}_{\mathit{c}}$, which decreases monotonously with increasing x up to \ensuremath{\sim}0.02 and then saturates around 90 K over the range 0.02\ensuremath{\lesssim}x\ensuremath{\le}0.1. The observed crossover from two- to one- (or lower-) dimensional behavior with increasing Ni dopant level may be related to a fractal nature for the system. The ${\mathit{T}}_{\mathit{c}}$ reduction of the present system is discussed from the standpoint of pair-breaking effects induced by the Ni doping.
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