Goitre in iodine in the soil. For example, in the English Midlands, the condition was known as Derbyshire Neck. In the United States, goitre was found in the Great Lakes, Midwest, and Intermountain regions. The condition now is practically absent in affluent nations, where table salt is supplemented with iodine. However, it is still prevalent in India, China, Central Asia, and Central Africa. Goitre had been prevalent in the alpine countries for a long time. Switzerland reduced the condition by introducing iodised salt in 1922. The Bavarian tracht in the Miesbach and Salzburg regions, which appeared in the 19th century, includes
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