Chemical substance made in a laboratory. Other chemical substances commonly encountered in pure form are diamond (carbon), gold, table salt (sodium chloride) and refined sugar (sucrose). However, in practice, no substance is entirely pure, and chemical purity is specified according to the intended use of the chemical. Chemical substances exist as solids, liquids, gases, or plasma, and may change between these phases of matter with changes in temperature or pressure. Chemical substances may be combined or converted to others by means of chemical reactions. Forms of energy, such as light and heat, are not matter, and are thus not "substances" in this
Pure subgroup Pure subgroup In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas. A subgroup formula_1 of a (typically abelian) group formula_2 is said to be pure if whenever an element of formula_1 has an formula_4 root in formula_2, it necessarily has an formula_4 root in formula_1. Formally, formula_8 is solvable in formula_2 formula_10 is solvable in formula_1. Pure subgroups are also called isolated subgroups or serving subgroups and were first investigated in Prüfer's 1923 paper