Cinnabar Cinnabar Cinnabar () and cinnabarite (), likely deriving from the ("kinnabari"), refer to the common bright scarlet to brick-red form of mercury(II) sulfide (HgS) that is the most common source ore for refining elemental mercury, and is the historic source for the brilliant red or scarlet pigment termed vermilion and associated red mercury pigments. Cinnabar generally occurs as a vein-filling mineral associated with recent volcanic activity and alkaline hot springs. The mineral resembles quartz in symmetry and in its exhibiting birefringence; cinnabar has a mean refractive index of approximately 3.2, a hardness between 2.0 and 2.5, and a specific gravity
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