Mineral Many sulfide minerals are economically important as metal ores; examples include sphalerite (ZnS), an ore of zinc, galena (PbS), an ore of lead, cinnabar (HgS), an ore of mercury, and molybdenite (MoS, an ore of molybdenum. Pyrite (FeS), is the most commonly occurring sulfide, and can be found in most geological environments. It is not, however, an ore of iron, but can be instead oxidized to produce sulfuric acid. Related to the sulfides are the rare sulfosalts, in which a metallic element is bonded to sulfur and a semimetal such as antimony, arsenic, or bismuth. Like the sulfides, sulfosalts are
Ore extension which means that "δ" is a homomorphism of abelian groups satisfying Then the Ore extension "R"["x";"σ","δ"], also called a skew polynomial ring, is the noncommutative ring obtained by giving the ring of polynomials "R"["x"] a new multiplication, subject to the identity If "δ" = 0 (i.e., is the zero map) then the Ore extension is denoted "R"["x"; "σ"]. If "σ" = 1 (i.e., the identity map) then the Ore extension is denoted "R"["x","δ"] and is called a differential polynomial ring. The Weyl algebras are Ore extensions, with "R" any commutative polynomial ring, "σ" the identity ring endomorphism, and "δ" the