Acknowledgement
Supported by : National Natural Science Foundation of China, Guangxi Natural Science Foundation
References
- F. A. A. Almahdi, M. Tamekkante, and R. A. K. Assaad, On the right orthogonal complement of the class of w-flat modules, J. Ramanujan Math. Soc. 33 (2018), no. 2, 159-175.
- S. Bazzoni and L. Positselski, S-almost perfect commutative rings, Preprint arXiv: 1801.04820, 2018.
- S. Bazzoni and L. Salce, On strongly flat modules over integral domains, Rocky Mountain J. Math. 34 (2004), no. 2, 417-439. https://doi.org/10.1216/rmjm/1181069861
- L. Fuchs and L. Salce, Modules over Non-Noetherian Domains, Mathematical Surveys and Monographs, 84, American Mathematical Society, Providence, RI, 2001.
- I. Kaplansky, The homological dimension of a quotient field, Nagoya Math. J. 27 (1966), 139-142. http://projecteuclid.org/euclid.nmj/1118801622 https://doi.org/10.1017/S0027763000011946
- H. Kim and F. Wang, On LCM-stable modules, J. Algebra Appl. 13 (2014), no. 4, 1350133, 18 pp. https://doi.org/10.1142/S0219498813501338
- S. Lee, h-divisible modules, Comm. Algebra 31 (2003), no. 1, 513-525. https://doi.org/10.1081/AGB-120016774
- S. Lee, Strongly flat modules over Matlis domains, Comm. Algebra 43 (2015), no. 3, 1232-1240. https://doi.org/10.1080/00927872.2013.851203
- E. Matlis, Divisible modules, Proc. Amer. Math. Soc. 11 (1960), 385-391. https://doi.org/10.2307/2034781
- E. Matlis, Cotorsion modules, Mem. Amer. Math. Soc. No. 49 (1964), 66 pp.
- A. Mimouni, Integral domains in which each ideal is a W-ideal, Comm. Algebra 33 (2005), no. 5, 1345-1355. https://doi.org/10.1081/AGB-200058369
- L. Positselski and A. Slavik, On strongly flat and weakly cotorsion modules, Math. Z. 291 (2019), no. 3, pp. 831-875. https://doi.org/10.1007/s00209-018-2116-z
- Y. Pu, G. Tang, and F. Wang, Pullbacks of C-hereditary domains, Bull. Korean Math. Soc. 55 (2018), no. 4, 1093-1101. https://doi.org/10.4134/BKMS.b170600
- F. Wang, Finitely presented type modules and w-coherent rings, J. Sichuan Normal Univ. 33 (2010), 1-9. https://doi.org/10.3969/j.issn.1001-8395.2010.01.001
- F. Wang, On w-projective modules and w-flat modules, Algebra Colloq. 4 (1997), no. 1, 111-120.
- F. Wang and H. Kim, w-injective modules and w-semi-hereditary rings, J. Korean Math. Soc. 51 (2014), no. 3, 509-525. https://doi.org/10.4134/JKMS.2014.51.3.509
- F. Wang and H. Kim, Two generalizations of projective modules and their applications, J. Pure Appl. Algebra 219 (2015), no. 6, 2099-2123. https://doi.org/10.1016/j.jpaa.2014.07.025
- F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016. https://doi.org/10.1007/978-981-10-3337-7
- F. Wang and L. Qiao, The w-weak global dimension of commutative rings, Bull. Korean Math. Soc. 52 (2015), no. 4, 1327-1338. https://doi.org/10.4134/BKMS.2015.52.4.1327
- F. Wang and L. Qiao, A homological characterization of Krull domains II, Comm. Algebra, (to appear).
- F. G. Wang and J. Zhang, Injective modules over w-Noetherian rings, Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 6, 1119-1130.
- F. G. Wang and D. C. Zhou, A homological characterization of Krull domains, Bull. Korean Math. Soc. 55 (2018), no. 2, 649-657. https://doi.org/10.4134/BKMS.b170203
- H. Yin, F. Wang, X. Zhu, and Y. Chen, w-modules over commutative rings, J. Korean Math. Soc. 48 (2011), no. 1, 207-222. https://doi.org/10.4134/JKMS.2011.48.1.207
- S. Zhao, F. Wang, and H. Chen, Flat modules over a commutative ring are w-modules, J. Sichuan Normal Univ. 35 (2012), 364-366. https://doi.org/10.3969/j.issn.1001-8395.2012.03.016