Cinnabar of approximately 8.1. The color and properties derive from a structure that is a hexagonal crystalline lattice belonging to the trigonal crystal system, crystals that sometimes exhibit twinning. Cinnabar has been used for its color since antiquity in the Near East, including as a rouge-type cosmetic, in the New World since the Olmec culture, and in China since as early as the Yangshao culture, where it was used in coloring stoneware. Associated modern precautions for use and handling of cinnabar arise from the toxicity of the mercury component, which was recognized as early as ancient Rome. The name comes from
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