Completion of a Prufer domain

被引：10

作者：

Kang, BG ^{[1
]}

Park, MH ^{[1
]}

机构：

[1] Pohang Inst Sci & Technol, Dept Math, Pohang 790784, South Korea

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 1999年 / 140卷 / 02期

关键词：

D O I：

10.1016/S0022-4049(97)00212-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let V (resp. D) be a valuation domain (resp. SFT Prufer domain), I a proper ideal, and (V) over cap (resp. (D) over cap) be the I-adic completion of V (resp. D). We show that (1) (V) over cap is a valuation domain, (2) Krull dimension of (V) over cap dim V/I + 1 if I is not idempotent, (V) over cap congruent to V/I if I is idempotent, (3) dim (D) over cap = dimD/I + 1, (4)(D) over cap is an SFT Prufer ring, and (5) (D) over cap is a catenarian ring. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：125 / 135

页数：11

共 9 条

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Kang, BG
Park, MH
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