Chalcopyrite Chalcopyrite Chalcopyrite ( ) is a copper iron sulfide mineral that crystallizes in the tetragonal system. It has the chemical formula CuFeS. It has a brassy to golden yellow color and a hardness of 3.5 to 4 on the Mohs scale. Its streak is diagnostic as green tinged black. On exposure to air, chalcopyrite oxidises to a variety of oxides, hydroxides and sulfates. Associated copper minerals include the sulfides bornite (CuFeS), chalcocite (CuS), covellite (CuS), digenite (CuS); carbonates such as malachite and azurite, and rarely oxides such as cuprite (CuO). Chalcopyrite is rarely found in association with native copper. Natural
Ore condition condition ensures "R" is an essential submodule of "D". Lastly, there is even an example of a domain in a division ring which satisfies "neither" Ore condition (see examples below). Another natural question is: "When is a subring of a division ring right Ore?" One characterization is that a subring "R" of a division ring "D" is a right Ore domain if and only if "D" is a flat left "R"-module . A different, stronger version of the Ore conditions is usually given for the case where "R" is not a domain, namely that there should be a common multiple