About: Complete intersection ring

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In commutative algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally, they can be thought of roughly as the local rings that can be defined using the "minimum possible" number of relations. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ ⊃ regular local rings

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  • In commutative algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally, they can be thought of roughly as the local rings that can be defined using the "minimum possible" number of relations. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ ⊃ regular local rings (en)
  • 可換環論の完全交叉環（かんぜんこうさかん、英: complete intersection ring）とは、する代数多様体の座標環のような性質を持つように定義された可換環のことである。簡単にいうと、必要最小限の個数の関係式で定義可能な局所環と考えられるものである。完交環ともいう。 ネーター局所環については次の包含関係が成り立つ。 強鎖状環 ⊃ コーエン・マコーレー環 ⊃ ゴレンシュタイン環 ⊃ 完全交叉環 ⊃ 正則局所環 (ja)
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  • In commutative algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally, they can be thought of roughly as the local rings that can be defined using the "minimum possible" number of relations. For Noetherian local rings, there is the following chain of inclusions: Universally catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ ⊃ regular local rings (en)
  • 可換環論の完全交叉環（かんぜんこうさかん、英: complete intersection ring）とは、する代数多様体の座標環のような性質を持つように定義された可換環のことである。簡単にいうと、必要最小限の個数の関係式で定義可能な局所環と考えられるものである。完交環ともいう。 ネーター局所環については次の包含関係が成り立つ。 強鎖状環 ⊃ コーエン・マコーレー環 ⊃ ゴレンシュタイン環 ⊃ 完全交叉環 ⊃ 正則局所環 (ja)
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  • Complete intersection ring (en)
  • 完全交叉環 (ja)
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