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A homomorphism between two algebras, ''A'' and ''B'', over a field (or ring) ''K'', is a map such that for all ''k'' in ''K'' and ''x'',''y'' in ''A'', * ''F''(''kx'') = ''kF''(''x'') * ''F''(''x'' + ''y'') = ''F''(''x'') + ''F''(''y'') * ''F''(''xy'') = ''F''(''x'')''F''(''y'') If ''F'' is bijective then ''F'' is said to be an isomorphism between ''A'' and ''B''. A common abbreviation for "homomorphism between algebras" is "algebra homomorphism" or "algebra map". Every algebra homomorphism is a homomorphism of ''K''-modules. == Unital algebra homomorphisms == If ''A'' and ''B'' are two unital algebras, then an algebra homomorphism is said to be ''unital'' if it maps the unity of ''A'' to the unity of ''B''. Often the words "algebra homomorphism" are actually used in the meaning of "unital algebra homomorphism", so non-unital algebra homomorphisms are excluded. A unital algebra homomorphism is a ring homomorphism. 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「algebra homomorphism」の詳細全文を読む スポンサード リンク
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