Goitre an underactive thyroid, thyroid supplements are used as treatment. Sometimes a partial or complete thyroidectomy is required. Goitre is more common among women, but this includes the many types of goitre caused by autoimmune problems, and not only those caused by simple lack of iodine. Chinese physicians of the Tang Dynasty (618–907) were the first to successfully treat patients with goitre by using the iodine-rich thyroid gland of animals such as sheep and pigs—in raw, pill, or powdered form. This was outlined in Zhen Quan's (d. 643 AD) book, as well as several others. One Chinese book, "The Pharmacopoeia of
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