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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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참고문헌 (35)
참고문헌 신청
A. Mimouni / 2003 / TW-domains and strong Mori domains / J. Pure Appl. Algebra 177 (1) : 79 ~ 93
A. Mimouni / 2005 / Integral domains in which each ideal is a W-ideal / Comm. Algebra 33 (5) : 1345 ~ 1355
B. G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 (1) : 151 ~ 170
D. Bennis / 2010 / A note on Gorenstein global dimension of pullback rings / Int. Electron. J. Algebra 8 : 30 ~ 44
D. D. Anderson / 1988 / Star-operations induced by overrings / Comm. Algebra 16 (12) : 2535 ~ 2553
A. Mimouni / 2005 / Integral domains in which each ideal is a W-ideal / Comm. Algebra 33 (5) : 1345 ~ 1355
B. G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 (1) : 151 ~ 170
D. Bennis / 2010 / A note on Gorenstein global dimension of pullback rings / Int. Electron. J. Algebra 8 : 30 ~ 44
D. D. Anderson / 1988 / Star-operations induced by overrings / Comm. Algebra 16 (12) : 2535 ~ 2553
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