Micronutrient deficiency Micronutrient deficiency Micronutrient deficiency or dietary deficiency is not enough of one or more of the micronutrients required for optimal plant or animal health. In humans and other animals they include both vitamin deficiencies and mineral deficiencies, whereas in plants the term refers to deficiencies of essential trace minerals. Micronutrient deficiencies affect more than two billion people of all ages in both developing and industrialized countries. They are the cause of some diseases, exacerbate others and are recognized as having an important impact on worldwide health. Important micronutrients include iodine, iron, zinc, calcium, selenium, fluorine, and vitamins A, B, B,
Trace field of a representation algebra formula_12 is then as simple as possible, more precisely: The algebra formula_12 is called the quaternion algebra of formula_4. The quaternion algebra of formula_7 is called the "invariant quaternion algebra" of formula_4, denoted by formula_24. As for trace fields, the former is not the same for all groups in the same commensurability class but the latter is. If formula_4 is an arithmetic Fuchsian group then formula_26 and formula_24 together are a number field and quaternion algebra from which a group commensurable to formula_4 may be derived. The theory for Kleinian groups (discrete subgroups of formula_29) is mostly similar as