J. Korean Math. Soc. 2017; 54(1): 35-57
Online first article August 25, 2016 Printed January 1, 2017
https://doi.org/10.4134/JKMS.j150582
Copyright © The Korean Mathematical Society.
Lei Qiao and Fanggui Wang
Sichuan Normal University, Sichuan Normal University
In this paper, we study the naturalstar-operation defined by the set of associated primes of principal ideals of an integral domain, which is called the $g$-operation. We are mainly concerned with the ideal-theoretic properties of this star-operation. In particular, we investigate DG-domains (i.e., integral domains in which each ideal is a $g$-ideal), which form a proper subclass of the DW-domains. In order to provide some original examples, we examine the transfer of the DG-property to pullbacks. As an application of the $g$-operation, it is shown that $w$-divisorial Mori domains can be seen as a Gorenstein analogue of Krull domains.
Keywords: $w$-operations, $g$-operations, DW-domains, DG-domains, pull\-backs
MSC numbers: 13A15, 13G05, 13F05
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