On Relative Injective Modules and Relative Coherent Rings

Communications in Algebra

Volumn 34, Issue 7, 2006, Pages 2531-2545

  Mao, Lixin ^a,b   Ding, Nanqing ^b  

^a NANJING INSTITUTE OF TECHNOLOGY   (China)

^b NANJING UNIVERSITY   (China)

Author keywords

( m, n ) coherent ring; ( m, n ) cotorsion module; ( m, n ) flat module; ( m, n ) injective module; ( m, n ) projective module; Cotorsion theory; Preenvelope

Indexed keywords

EID: 33745621885     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927870600651208     Document Type: Article

References (23)

1. Anderson, F. W., Fuller, K. R. (1974). Rings and Categories of Modules. New York: Springer-Verlag.
2. Asensio Mayor, J., Martinez Hernandez, J. (1988). Flat envelopes in commutative rings. Israel J. Math. 62(1):123-128.
3. Bican, L., Bashir, E., Enochs, E. E. (2001). All modules have flat covers. Bull. London Math. Soc. 33(4):385-390.
4. Björk, J. E. (1970). Rings satisfying certain chain conditions. J. Reine Angew Math. 245(10):63-73.
5. Chen, J. L., Ding, N. Q. (1996). On n-coherent rings. Comm. Algebra 24:3211-3216.
6. Chen, J. L., Ding, N. Q., Li, Y. L., Zhou, Y. Q. (2001). On (m, n)-injectivity of modules. Comm. Algebra 29(12):5589-5603.
7. Colby, R. R. (1975). Rings which have flat injective modules. J. Algebra 35:239-252.
8. Eklof, P. C., Trlifaj, J. (2001). How to make Ext vanish. Bull. London Math. Soc. 33(1):41-51.
9. Enochs, E. E. (1981). Injective and flat covers, envelopes and resolvents. Israel J. Math. 39(3):189-209.
10. Enochs, E. E., Jenda, O. M. G. (2000). Relative Homological Algebra. Berlin-New York: Walter de Gruyter.
11. Enochs, E. E., Jenda, O. M. G. Lopez-Ramos, J. A. (2004). The existence of Gorenstein flat covers. Math. Scand. 94(1):46-62.
12. Garcia Rozas, J. R., Torrecillas, B. (1994). Relative injective covers. Comm. Algebra 22:2925-2940.
13. Glaz, S. (1989). Commutative Coherent Rings. Lecture Notes in Math. 1371. Springer-Verlag.
14. Gupta, R. N. (1969). On f-injective modules and semihereditary rings. Proc. Nat. Inst. Sci. India Part A 35:323-328.
15. Jain, S. (1973). Flat and FP-injectivity. Proc. Amer. Math. Soc. 41(2):437-442.
16. Lam, T. Y. (1999). Lectures on Modules and Rings. New York-Heidelberg-Berlin: Springer-Verlag.
17. Rotman, J. J. (1979). An Introduction to Homological Algebra. New York: Academic Press.
18. Shamsuddin, A. (2001). n-injective and n-flat modules. Comm. Algebra 29(5):2039-2050.
19. Trlifaj, J. (2000). Covers, Envelopes, and Cotorsion Theories. Lecture notes for the workshop, "Homological Methods in Module Theory" Cortona, September 10-16.
20. Wisbauer, R. (1991). Foundations of Module and Ring Theory. Gordon and Breach.
21. Xu, J. (1996). Flat Covers of Modules. Lecture Notes in Math. Vol. 1634. Berlin-Heidelberg-New York: Springer Verlag.
22. Zhang, X. X., Chen, J. L., Zhang, J. (2005). On (m, n)-injective modules and (m, n)-coherent rings. Algebra Colloq. 12(1):149-160.
23. Zimmermann, W. (1977). Rein injektive direkte Summanden von moduln. Comm. Algebra 5:1083-1117.