Abstract
It was shown by Kang (1989) that a domain is a Krull domain if and only if is a Mori domain and a PMD. In this paper, we extend this result to Gorenstein multiplicative ideal theory. To do this, we introduce the concepts of -domains and G-PMDs, and study them by a new star-operation, i.e., the -operation. We prove that (1) a domain is an integrally closed -domain if and only if is a -domain; (2) a domain is a G-PMD if and only if is a -coherent -domain; (3) a domain is a G-Krull domain if and only if is a Mori domain and a G-P$v$MD.
Citation
Shiqi Xing. "-domains and Gorenstein Prüfer -multiplication domains." J. Commut. Algebra 13 (2) 263 - 279, Summer 2021. https://doi.org/10.1216/jca.2021.13.263
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