A characterization of Gorenstein Dedekind domains

Year 2017, , 97 - 102, 11.07.2017

Tao Xiong

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.

Keywords

Gorenstein Dedekind domain, divisible module

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.