Maximal non-integrally closed subrings of an integral domain

被引：2

作者：

Jarboui, Noomen ^{[1
,2
]}

Aljubran, Suaad ^{[1
]}

机构：

[1] King Faisal Univ, Dept Math & Stat, Coll Sci, POB 400, Al Hasa 31982, Saudi Arabia

[2] Univ Sfax, Fac Sci Sfax, Dept Math, Route Soukra,POB 1171, Sfax 3038, Tunisia

来源：

RICERCHE DI MATEMATICA | 2022年 / 71卷 / 02期

关键词：

Integral domain; Intermediate ring; Overring; Ring extension; Integral extension; Minimal extension; Integrally closed; Prufer domain; Valuation domain; Normal pair of rings; NORMAL PAIRS; FINITENESS CONDITIONS; RING EXTENSIONS; OVERRINGS; SET;

D O I：

10.1007/s11587-020-00500-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R subset of S be an extension of integral domains. The domain R is said to be a maximal non-integrally closed subring of S if R is not integrally closed in S, while each subring of S properly containing R is integrally closed in S. Jaballah (J Algebra Appl 11(5):1250041, 18pp, 2012) has characterized these domains when S is the quotient field of R. The main purpose of this paper is to study this kind of ring extensions in the general case. Some examples are provided to illustrate our obtained results. Our main result also answers a key question raised by Gilmer and Heinzer (J Math Kyoto Univ 7(2):133-150, 1967).

引用

页码：325 / 332

页数：8

共 23 条

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