Answer is: calcite and dolomite.
Non-silicate mineral is mineral that does not hold the silica tetrahedron. Carbonate anion is CO₃²⁻.
Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO₃).
Dolomite is an carbonate mineral composed of calcium magnesium carbonate (CaMg(CO₃)₂).