ft -定义域和Gorenstein prfer v乘定义域

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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