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 condition Ore condition In mathematics, especially in the area of algebra known as ring theory, the Ore condition is a condition introduced by Øystein Ore, in connection with the question of extending beyond commutative rings the construction of a field of fractions, or more generally localization of a ring. The "right Ore condition" for a multiplicative subset "S" of a ring "R" is that for and , the intersection . A (non-commutative) integral domain for which the set of non-zero elements satisfies the right Ore condition is called a right Ore domain. The left case is defined similarly. The goal is