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Let $R$ be a Ding-Chen ring. Yang \cite{Yang2012} and Zhang \cite{Zhang2015} asked whether or not every $R$-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modul\-es have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.
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참고문헌 (25)
참고문헌 신청
Chunxia Zhang / 2015 / RELATIVE AND TATE COHOMOLOGY OF DING MODULES AND COMPLEXES / 대한수학회지 52 (4) : 821 ~ 838
D. Bennis / 2006 / Gorenstein homological dimensions of commutative rings, un-published manuscript / arXiv:math/0611358v1
D. Bennis / 2009 / Rings over which the class of Gorenstein at modules is closed under exten-sions / Comm. Algebra 37 (3) : 855 ~ 868
D. Bennis / 2010 / Global Gorenstein dimensions / Proc. Amer. Math. Soc 138 (2) : 461 ~ 465
D. Bennis / 2011 / A note on Gorenstein at dimension / Algebra Colloq 18 (1) : 155 ~ 161
D. Bennis / 2006 / Gorenstein homological dimensions of commutative rings, un-published manuscript / arXiv:math/0611358v1
D. Bennis / 2009 / Rings over which the class of Gorenstein at modules is closed under exten-sions / Comm. Algebra 37 (3) : 855 ~ 868
D. Bennis / 2010 / Global Gorenstein dimensions / Proc. Amer. Math. Soc 138 (2) : 461 ~ 465
D. Bennis / 2011 / A note on Gorenstein at dimension / Algebra Colloq 18 (1) : 155 ~ 161
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