In an attempt to extend the chemistry of Ag(II) compounds to novel ligand environments, we have examined various polymorphs of an as yet unknown compound of AgSO(4) stoichiometry by means of a quantum chemistry DFT approach. Since AgSO(4) has not yet been prepared, we were interested whether genuine divalent silver, Ag(II), could be stabilized in the presence of sulfate (SO(4)(2-)) anions or whether it would rather have a tendency toward disproportionation to Ag(I)/Ag(III) (as known from binary oxide, "AgO") or maybe toward the formation of peroxodisulfate (S(2)O(8)(2-)) of Ag(I). Considering all important electromeric forms, Ag(II)SO(4), Ag(I)Ag(III)(SO(4))(2), and Ag(I)(2)S(2)O(8), in a variety of crystal structures, we examined their dynamical (vibrational) stability and discussed the most stable phases from the point of view of structural features thought to be crucial for appearance of high-T(C) superconductivity. We show that a compound of a nominal stoichiometry, AgSO(4), should most likely be a genuine paramagnetic sulfate of divalent silver which forms 3D ...Ag-O-S(O(2))-O... networks, and--unlike CuSO(4)--shows no direct connections of paramagnetic Ag(II) centers via Ag-O bridges. This must lead to low electronic dimensionality and concomitant low potential for the appearance of high-T(C) superconductivity. Finally, we discuss structural features of the most stable phase of AgSO(4) predicted here in a broader context of crystal structures of group 11 metals.