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A characterization of Gorenstein Dedekind domains

Year 2017, , 97 - 102, 11.07.2017
https://doi.org/10.24330/ieja.325929

Abstract

In this paper, we show that a domain $R$ is a Gorenstein Dedekind
domain if and only if every divisible module is Gorenstein
injective; if and only if every divisible module is copure
injective.

References

  • S. Bazzoni and L. Salce, Almost perfect domains, Colloq. Math., 95(2) (2003), 285-301.
  • D. Bennis, A short survey on Gorenstein global dimension, Actes des rencontres du C.I.R.M., 2(2) (2010), 115-117.
  • D. Bennis and N. Mahdou, Global Gorenstein dimensions, Proc. Amer. Math. Soc., 138(2) (2010), 461-465.
  • E. E. Enochs and O. M. G. Jenda, Copure injective resolutions, at resolvents and dimensions, Comment. Math. Univ. Carolin., 34(2) (1993), 203-211.
  • E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z., 220(4) (1995), 611-633.
  • E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Exp. Math., Vol. 30, Walter de Gruyter, Berlin, 2000.
  • X. H. Fu, H. Y. Zhu and N. Q. Ding, On copure projective modules and copure projective dimensions, Comm. Algebra, 40(1) (2012), 343-359.
  • L. Fuchs and S. B. Lee, Weak-injectivity and almost perfect domains, J. Algebra, 321(1) (2009), 18-27.
  • R. Hamsher, On the structure of a one dimensional quotient field, J. Algebra, 19 (1971), 416-425.
  • S. B. Lee, h-Divisible modules, Comm. Algebra, 31(1) (2003), 513-525.
  • S. B. Lee, Weak-injective modules, Comm. Algebra, 34(1) (2006), 361-370.
Year 2017, , 97 - 102, 11.07.2017
https://doi.org/10.24330/ieja.325929

Abstract

References

  • S. Bazzoni and L. Salce, Almost perfect domains, Colloq. Math., 95(2) (2003), 285-301.
  • D. Bennis, A short survey on Gorenstein global dimension, Actes des rencontres du C.I.R.M., 2(2) (2010), 115-117.
  • D. Bennis and N. Mahdou, Global Gorenstein dimensions, Proc. Amer. Math. Soc., 138(2) (2010), 461-465.
  • E. E. Enochs and O. M. G. Jenda, Copure injective resolutions, at resolvents and dimensions, Comment. Math. Univ. Carolin., 34(2) (1993), 203-211.
  • E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z., 220(4) (1995), 611-633.
  • E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Exp. Math., Vol. 30, Walter de Gruyter, Berlin, 2000.
  • X. H. Fu, H. Y. Zhu and N. Q. Ding, On copure projective modules and copure projective dimensions, Comm. Algebra, 40(1) (2012), 343-359.
  • L. Fuchs and S. B. Lee, Weak-injectivity and almost perfect domains, J. Algebra, 321(1) (2009), 18-27.
  • R. Hamsher, On the structure of a one dimensional quotient field, J. Algebra, 19 (1971), 416-425.
  • S. B. Lee, h-Divisible modules, Comm. Algebra, 31(1) (2003), 513-525.
  • S. B. Lee, Weak-injective modules, Comm. Algebra, 34(1) (2006), 361-370.
There are 11 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Articles
Authors

Tao Xiong This is me

Publication Date July 11, 2017
Published in Issue Year 2017

Cite

APA Xiong, T. (2017). A characterization of Gorenstein Dedekind domains. International Electronic Journal of Algebra, 22(22), 97-102. https://doi.org/10.24330/ieja.325929
AMA Xiong T. A characterization of Gorenstein Dedekind domains. IEJA. July 2017;22(22):97-102. doi:10.24330/ieja.325929
Chicago Xiong, Tao. “A Characterization of Gorenstein Dedekind Domains”. International Electronic Journal of Algebra 22, no. 22 (July 2017): 97-102. https://doi.org/10.24330/ieja.325929.
EndNote Xiong T (July 1, 2017) A characterization of Gorenstein Dedekind domains. International Electronic Journal of Algebra 22 22 97–102.
IEEE T. Xiong, “A characterization of Gorenstein Dedekind domains”, IEJA, vol. 22, no. 22, pp. 97–102, 2017, doi: 10.24330/ieja.325929.
ISNAD Xiong, Tao. “A Characterization of Gorenstein Dedekind Domains”. International Electronic Journal of Algebra 22/22 (July 2017), 97-102. https://doi.org/10.24330/ieja.325929.
JAMA Xiong T. A characterization of Gorenstein Dedekind domains. IEJA. 2017;22:97–102.
MLA Xiong, Tao. “A Characterization of Gorenstein Dedekind Domains”. International Electronic Journal of Algebra, vol. 22, no. 22, 2017, pp. 97-102, doi:10.24330/ieja.325929.
Vancouver Xiong T. A characterization of Gorenstein Dedekind domains. IEJA. 2017;22(22):97-102.