Maximal non-integrally closed subrings of an integral domain

被引：0
作者：
Noômen Jarboui
Suaad Aljubran
机构：
[1] King Faisal University,Department of Mathematics and Statistics, College of Science
[2] Université de Sfax,Département de Mathématiques, Faculté des Sciences de Sfax
来源：
Ricerche di Matematica | 2022年 / 71卷
关键词：
Integral domain; Intermediate ring; Overring; Ring extension; Integral extension; Minimal extension; Integrally closed; Prüfer domain; Valuation domain; Normal pair of rings; Primary 13B02; Secondary 13C15; 13A17; 13A18; 13B25; 13E05;
D O I：
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摘要：
Let R⊂S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\subset S$$\end{document} 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).
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页码：325 / 332
页数：7
相关论文
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