On the Ideal Theory of the Kronecker Function Ring and the Domain D(X)

Author:

Arnold Jimmy T.

Abstract

Let D be an integrally closed domain with identity having quotient field L. If {Vα} is the set of valuation overrings of D and if A is an ideal of D, then à = ∪ αAVα is an ideal of D called the completion of A. If X is an indeterminate over D and fD[X], then we denote by Af the ideal of D generated by the coefficients of f. The Kronecker function ring DK of D is defined by DK = {f/g| f, gD[X], ÃfAg} (4, p. 558); and the domain D(X) is defined by D(X) = {f/g| f, gD[X], Ag = D} (5, p. 17). In this paper we wish to relate the ideal theory of D to that of DK and D(X) for the case in which D is a Prüfer domain, a Dedekind domain, or an almost Dedekind domain.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 52 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Rings with S-Noetherian spectrum;Journal of Algebra and Its Applications;2024-01-31

2. Non-integrally closed Kronecker function rings and integral domains with a unique minimal overring;Annali di Matematica Pura ed Applicata (1923 -);2023-12-14

3. PRIME FACTORIZATION OF IDEALS IN COMMUTATIVE RINGS, WITH A FOCUS ON KRULL RINGS;J KOREAN MATH SOC;2023

4. Invertibility, Semistar Operations, and the Ring of Finite Fractions;Algebraic, Number Theoretic, and Topological Aspects of Ring Theory;2023

5. S-Noetherian Modules and Rings;Chain Conditions in Commutative Rings;2022

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3