Native metal brass, bronze, pewter, German silver, osmiridium, electrum, white gold, and silver-mercury and gold-mercury amalgam. Only gold, silver, copper and the platinum metals occur in nature in large amounts. Over geological time scales, very few metals can resist natural weathering processes like oxidation, which is why generally only the less reactive metals such as gold and platinum are found as native metals. The others usually occur as isolated pockets where a natural chemical process reduces a common compound or ore of the metal, leaving the pure metal behind as small flakes or inclusions. Non-metallic elements occurring in the native state include
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