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In this paper, we mainly discuss Gorenstein Dedekind domains (G-Dedekind domains for short) and their overrings. Let R be a one-dimensional Noetherian domain with quotient field K and integral closure T. Then it is proved that R is a G-Dedekind domain if and only if for any prime ideal P of R which contains (R:KT), P is Gorenstein projective. We also give not only an example to show that G-Dedekind domains are not necessarily Noetherian Warfield domains, but also a definition for a special kind of domain: a 2-DVR. As an application, we prove that a Noetherian domain R is a Warfield domain if and only if for any maximal ideal M of R, RM is a 2-DVR.
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참고문헌 (20)
참고문헌 신청
D. Bennis / 2007 / Strongly Gorenstein projective, injective, and flat modules / J. Pure Appl. Algebra 210 (2) : 437 ~ 445
D. Bennis / 2009 / A generalization of strongly Gorenstein projective modules / J. Algebra Appl 8 (2) : 219 ~ 227
D. Bennis / 2010 / A note on Gorenstein global dimension of pullback rings / Int. Electron. J. Algebra 8 : 30 ~ 44
D. Bennis / 2010 / Global Gorenstein dimensions / Proc. Amer. Math. Soc 138 (2) : 461 ~ 465
E. Matlis / 1970 / The two-generator problem for ideals / Michigan Math. J 17 : 257 ~ 265
D. Bennis / 2009 / A generalization of strongly Gorenstein projective modules / J. Algebra Appl 8 (2) : 219 ~ 227
D. Bennis / 2010 / A note on Gorenstein global dimension of pullback rings / Int. Electron. J. Algebra 8 : 30 ~ 44
D. Bennis / 2010 / Global Gorenstein dimensions / Proc. Amer. Math. Soc 138 (2) : 461 ~ 465
E. Matlis / 1970 / The two-generator problem for ideals / Michigan Math. J 17 : 257 ~ 265
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