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A multiplicative character (or linear character, or simply character) on a group ''G'' is a group homomorphism from ''G'' to the multiplicative group of a field , usually the field of complex numbers. If ''G'' is any group, then the set Ch(''G'') of these morphisms forms an abelian group under pointwise multiplication. This group is referred to as the character group of ''G''. Sometimes only ''unitary'' characters are considered (thus the image is in the unit circle); other such homomorphisms are then called ''quasi-characters''. Dirichlet characters can be seen as a special case of this definition. Multiplicative characters are linearly independent, i.e. if are different characters on a group ''G'' then from it follows that . ==Examples== *Consider the (''ax'' + ''b'')-group :: : Functions ''f''''u'' : ''G'' → C such that where ''u'' ranges over complex numbers C are multiplicative characters. * Consider the multiplicative group of positive real numbers (R+,·). Then functions ''f''''u'' : (R+,·) → C such that ''f''''u''(''a'') = ''a''''u'', where ''a'' is an element of (R+, ·) and ''u'' ranges over complex numbers C, are multiplicative characters. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「multiplicative character」の詳細全文を読む スポンサード リンク
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