赋值环
在抽象代数中,赋值环是一个域里的一类特别子环,可由域上的某个赋值定义。离散赋值环是其中较容易操作的一类。
赋值环是一个整环D的分式域 F的元素x,至少x 或 x ∈ D.
一个域 F 的子环 R 被称作赋值环,若且唯若对每个 ,必有
或
。R被称作其分式域 F赋值环或被称作在其分式域 F的素点(位)
若 R 是主理想域,此时 R 被称为离散赋值环。
单词 | Valuation ring |
释义 |
Valuation ring
中文百科
赋值环在抽象代数中,赋值环是一个域里的一类特别子环,可由域上的某个赋值定义。离散赋值环是其中较容易操作的一类。 赋值环是一个整环D的分式域 F的元素x,至少x 或 x ∈ D.
一个域 F 的子环 R 被称作赋值环,若且唯若对每个 若 R 是主理想域,此时 R 被称为离散赋值环。
英语百科
Valuation ring 赋值环In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F, at least one of x or x belongs to D. Given a field F, if D is a subring of F such that either x or x belongs to D for every nonzero x in F, then D is said to be a valuation ring for the field F or a place of F. Since F in this case is indeed the field of fractions of D, a valuation ring for a field is a valuation ring. Another way to characterize the valuation rings of a field F is that valuation rings D of F have F as their field of fractions, and their ideals are totally ordered by inclusion; or equivalently their principal ideals are totally ordered by inclusion. In particular, every valuation ring is a local ring. |
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