Ore be processed and what ore is of too low a grade to be worth mining. Metal ores are generally oxides, sulfides, silicates, or native metals (such as native copper) that are not commonly concentrated in the Earth's crust, or noble metals (not usually forming compounds) such as gold. The ores must be processed to extract the elements of interest from the waste rock and from the ore minerals. Ore bodies are formed by a variety of geological processes. The process of ore formation is called ore genesis. An ore deposit is an accumulation of ore. This is distinct from a
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