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Essential self-adjointness of n-dimensional Dirac operators with a variable mass termWe formulate a theorem saying that the Dirac operator corresponding to a one-electron atomic ion is essentially self-adjoint on the usual domain, provided that the nuclear charge Z is less than 118. Furthermore, for such nuclear charges the domains of the closure of the free particle and total Dirac operators are equal. In the present part I of this paper we prove this theorem for the part of the operator over each of the usual reducing subspaces.