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정칙렬 Reguläre Folge Regular sequence 正則列
rdfs:comment
In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This is the algebraic analogue of the geometric notion of a complete intersection. Reguläre Folgen spielen in kommutativen Algebra und der algebraischen Geometrie eine Rolle. Sie werden benötigt, um die Tiefe eines Moduls und Cohen-Macaulay-Ringe zu definieren und um Aussagen über vollständige Durchschnitte zu machen. Dieser Artikel beschäftigt sich mit kommutativer Algebra. Insbesondere sind alle betrachteten Ringe kommutativ und haben ein Einselement. Ringhomomorphismen bilden Einselemente auf Einselemente ab. Für weitere Details siehe Kommutative Algebra. 가환대수학에서 정칙렬(正則列, 영어: regular sequence 레귤러 시퀀스[*])은 어떤 가군의 크기를 하나씩 ‘최대한’ 줄이는, 가환환 원소들의 열이다.:123–152, Chapter 6 여기서 가군의 ‘크기를 줄인다’는 것은 가환환의 원소로 생성되는 부분 가군에 대한 몫가군을 취하는 것이다. 구체적으로, 정칙렬에서 임의의 성분 는 그 이전 성분들로 생성되는 부분 가군 에 대한 몫가군 의 영인자가 아니다. 대수기하학적으로, 정칙렬은 여차원을 양의 정수 만큼씩 줄이는 ‘잘라내기’들로서 정의되는 부분 대수다양체에 해당한다. 数学、特に可換環論において正則列(せいそくれつ、英: regular sequence)とは、不定元のように振る舞う可環環の元の列のことである。例えば、係数環 R を持つ多項式環 R[X1, ..., Xn] において X1, ..., Xn は正則列である。
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数学、特に可換環論において正則列(せいそくれつ、英: regular sequence)とは、不定元のように振る舞う可環環の元の列のことである。例えば、係数環 R を持つ多項式環 R[X1, ..., Xn] において X1, ..., Xn は正則列である。 가환대수학에서 정칙렬(正則列, 영어: regular sequence 레귤러 시퀀스[*])은 어떤 가군의 크기를 하나씩 ‘최대한’ 줄이는, 가환환 원소들의 열이다.:123–152, Chapter 6 여기서 가군의 ‘크기를 줄인다’는 것은 가환환의 원소로 생성되는 부분 가군에 대한 몫가군을 취하는 것이다. 구체적으로, 정칙렬에서 임의의 성분 는 그 이전 성분들로 생성되는 부분 가군 에 대한 몫가군 의 영인자가 아니다. 대수기하학적으로, 정칙렬은 여차원을 양의 정수 만큼씩 줄이는 ‘잘라내기’들로서 정의되는 부분 대수다양체에 해당한다. Reguläre Folgen spielen in kommutativen Algebra und der algebraischen Geometrie eine Rolle. Sie werden benötigt, um die Tiefe eines Moduls und Cohen-Macaulay-Ringe zu definieren und um Aussagen über vollständige Durchschnitte zu machen. Dieser Artikel beschäftigt sich mit kommutativer Algebra. Insbesondere sind alle betrachteten Ringe kommutativ und haben ein Einselement. Ringhomomorphismen bilden Einselemente auf Einselemente ab. Für weitere Details siehe Kommutative Algebra. In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This is the algebraic analogue of the geometric notion of a complete intersection.
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