# A HALF-CENTERED STAR-OPERATION ON AN INTEGRAL DOMAIN

• Qiao, Lei ;
• Wang, Fanggui
• Published : 2017.01.01
• 39 27

#### Abstract

In this paper, we study the natural star-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;pullbacks

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#### Acknowledgement

Supported by : NSFC, Doctorial Scientic Research Foundation, Sichuan Normal University, Sichuan Provincial Education Department