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The sum-rate capacity of a noncoherent memoryless multiple-access Rician fading channel is investigated under three different categories of power constraints: individual per user peak-power constraints, individual per user average-power constraints, or a global power-sharing average-power constraint. Upper and lower bounds on the sum-rate capacity are derived, and it is shown that at high signal-to-noise ratio the sum-rate capacity only grows double-logarithmically in the available power. The asymptotic behavior of capacity is then analyzed in detail and the exact asymptotic expansion is derived including its second term, the so-called fading number. It is shown that the fading number is identical to the fading number of the single-user Rician fading channel that is obtained when only the user seeing the best channel is transmitting and all other users are switched off at all times. This pessimistic result holds independently of the type of power constraint that is imposed.