Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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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.

A half-centered star-operation on an integral domain

Lei Qiao and Fanggui Wang

Sichuan Normal University, Sichuan Normal University

Abstract

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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