|
In abstract algebra, adjunction is a construction in field theory, where for a given field extension ''E''/''F'', subextensions between ''E'' and ''F'' are constructed. == Definition == Let ''E'' be a field extension of a field ''F''. Given a set of elements ''A'' in the larger field ''E'' we denote by ''F''(''A'') the smallest subextension which contains the elements of ''A''. We say ''F''(''A'') is constructed by adjunction of the elements ''A'' to ''F'' or generated by ''A''. If ''A'' is finite we say ''F''(''A'') is finitely generated and if ''A'' consists of a single element we say ''F''(''A'') is a simple extension. The primitive element theorem states a finite separable extension is simple. In a sense, a finitely generated extension is a transcendental generalization of a finite extension since, if the generators in ''A'' are all algebraic, then ''F''(''A'') is a finite extension of ''F''. Because of this, most examples come from algebraic geometry. A subextension of a finitely generated field extension is also a finitely generated extension.〔.〕 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「Adjunction (field theory)」の詳細全文を読む スポンサード リンク
|