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 with "u", "v" not zero divisors. In this case, Ore's theorem guarantees the existence of an over-ring called the (right or left) classical ring of quotients. Commutative domains are automatically Ore domains, since for nonzero "a" and "b", "ab" is nonzero in . Right Noetherian domains, such as right principal ideal domains, are also known to be right Ore domains. Even more generally, Alfred Goldie proved that a domain "R" is right Ore if and only if "R" has finite uniform dimension. It is also true that right Bézout domains are right Ore. A subdomain of a division ring which