Abstract
Let R be a commutative ring with identity. An R-module E is said to be weak injective if for any super finitely presented R-module N. In this article, for a domain R with quotient field
, it is characterized when K/R as an R-module is weak injective. Also, a couple of characterizations of generalized coherent domains of self-weak injective dimension one are given. As corollaries, we characterize Gorenstein Dedekind (resp., Gorenstein Prüfer) domains.
Acknowledgements
We would like to thank the referee for her/his valuable comments which improved the original version of this manuscript. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03033342).