Some Results on Noetherian Warfield Domains

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-01-13 DOI:10.1142/s1005386722000062

Kui Hu, J. Lim, D. Zhou

引用次数: 0

Abstract

Let [Formula: see text] be a domain. In this paper, we show that if [Formula: see text] is one-dimensional, then [Formula: see text] is a Noetherian Warfield domain if and only if every maximal ideal of [Formula: see text] is 2-generated and for every maximal ideal[Formula: see text] of [Formula: see text], [Formula: see text] is divisorial in the ring [Formula: see text]. We also prove that a Noetherian domain [Formula: see text] is a Noetherian Warfield domain if and only if for every maximal ideal [Formula: see text] of [Formula: see text], [Formula: see text] can be generated by two elements. Finally, we give a sufficient condition under which all ideals of [Formula: see text] are strongly Gorenstein projective.

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关于Noetherian Warfield域的一些结果

设[公式:见文本]为一个域。在本文中，我们证明了如果[公式:见文]是一维的，那么当且仅当[公式:见文]的每个极大理想[公式:见文]都是2生成的，并且对于[公式:见文]的每个极大理想[公式:见文]，[公式:见文]在环[公式:见文]中是可分的，[公式:见文]是Noetherian Warfield域。我们还证明了一个Noetherian域[公式:见文]是一个Noetherian Warfield域当且仅当对于[公式:见文]的每一个极大理想[公式:见文]，[公式:见文]可以由两个元素生成。最后，我们给出了一个充分条件，在此条件下[公式:见文]的所有理想都是强Gorenstein投影。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.