This work considers the uplink (UL) of a multi-cell massive MIMO system with $L$ cells, having each $K$ mono-antenna users communicating with an $N-$antennas base station (BS). The channel model involves Rician fading with distinct per-user Rician factors and channel correlation matrices and takes into account pilot contamination and imperfect CSI. The objective is to evaluate the performances of such systems with different single-cell and multi-cell detection methods. In the former, we investigate MRC and single-cell MMSE (S-MMSE); as to the latter, we are interested in multi-cell MMSE (M-MMSE) that was recently shown to provide unbounded rates in Rayleigh fading. The analysis is led assuming the infinite $N$ limit and yields informative closed-form approximations that are substantiated by a selection of numerical results for finite system dimensions. Accordingly, these expressions are accurate and provide relevant insights into the effects of the different system parameters on the overall performances.