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A HALF-CENTERED STAR-OPERATION ON AN INTEGRAL DOMAIN

Fanggui Wang|Lei Qiao
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회지 (Journal of the KMS)|제54권 제1호|pp. 35-57

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키워드

pullbacksw-operationsg-operationsDW-domainsDG-domains
주제분류수학

초록

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.

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.

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