ft -定义域和Gorenstein prfer v乘定义域

IF 0.3 4区数学 Q4 MATHEMATICS Journal of Commutative Algebra Pub Date : 2021-06-01 DOI:10.1216/jca.2021.13.263

Shiqi Xing

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引用次数: 2

摘要

Kang(1989)证明域R是Krull域当且仅当R是Mori域和PvMD。本文将这一结果推广到Gorenstein乘法理想理论中。为此，我们引入了ft -域和G-PvMDs的概念，并通过一种新的星型运算，即f运算来研究它们。证明(1)当且仅当R是p域时，定义域R是整闭ft域;(2)域R是G-PvMD当且仅当R是g相干ft域;(3)定义域R是G-Krull定义域当且仅当R是Mori定义域和G-Pv$v$MD。

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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FT-domains and Gorenstein Prüfer v-multiplication domains

It was shown by Kang (1989) that a domain R is a Krull domain if and only if R is a Mori domain and a PvMD. In this paper, we extend this result to Gorenstein multiplicative ideal theory. To do this, we introduce the concepts of FT-domains and G-PvMDs, and study them by a new star-operation, i.e., the f-operation. We prove that (1) a domain R is an integrally closed FT-domain if and only if R is a P-domain; (2) a domain R is a G-PvMD if and only if R is a g-coherent FT-domain; (3) a domain R is a G-Krull domain if and only if R is a Mori domain and a G-Pv$v$MD.

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来源期刊

Journal of Commutative Algebra MATHEMATICS-

CiteScore

0.80

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.

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