Properties of modules and rings relative to some matrices

Communications in Algebra

Volumn 36, Issue 10, 2008, Pages 3682-3707

  Zhang, Xiaoxiang ^a   Chen, Jianlong ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Relative coherence; Relative flatness; Relative injectivity

Indexed keywords

EID: 55049097110     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927870802157996     Document Type: Article

References (30)

1. Anderson, F. W., Fuller, K. R. (1993). Rings and Categories of Modules. New York: Springer-Verlag.
2. Angeleri-Hügel, L. (2003). Endocoherent modules. Pacific J. Math. 212:1-11.
3. Azumaya, G. (1987). Finite splitness and finite projectivity. J. Algebra 106:114-134.
4. Chen, J. L., Ding, N. Q., Li, Y. L., Zhou, Y. Q. (2001). On (m, n)-injectivity of modules. Comm. Algebra 29:5589-5603.
5. Chen, J. L., Zhou, Y. Q. (2006). Extensions of injectivity and coherent rings. Comm. Algebra 34:275-288.
6. Chen, J. L., Zhou, Y. Q., Zhu, Z. M. (2005). GP-injective rings need not be P-injective. Comm. Algebra 33:2395-2403.
7. -1-Projective Modules. Ph.D. thesis, Kent State University.
8. Dauns, J., Fuchs, L. (2004). Torsion-freeness in rings with zero-divisors. J. Algebra Appl. 3:221-237.
9. Ding, N. Q., Chen, J. L. (1993). Relative coherence and preenvelopes. Manuscripta Math. 81(3-4):243-262.
10. Enochs, E. E., Jenda, O. M. G. (2000). Relative Homological Algebra. de Gruyter Expositions in Math. 30. Berlin: de Gruyter.
11. Harada, M. (1982). Self mini-injective rings. Osaka J. Math. 19:587-597.
12. Jampachon, P., Ittharat, J., Sanh, N. V. (2000). On finite injectivity. Southeast Asian Bull. Math. 24:559-564.
13. Lam, T. Y. (1998). Lectures on Modules and Rings. New York: Springer-Verlag.
14. Mao, L. X., Tong, W. T. (2005). Quasi-mininjective modules (in Chinese). J. Math. Research and Exposition 25:369-375.
15. Mao, L. X., Ding, N. Q. (2006). On relative injective modules and relative coherent rings. Comm. Algebra 34:2531-2545.
16. Nicholson, W. K., Park, J. K., Yousif, M. F. (1999). Principally quasi-injective modules. Comm. Algebra 27:1683-1693.
17. Nicholson, W. K., Yousif, M. F. (1995). Principally injective rings. J. Algebra 174:77-93.
18. Nicholson, W. K., Yousif, M. F. (1997). Mininjective rings. J. Algebra 187:548-578.
19. Ramamurthi, V. S., Rangaswamy, K. M. (1973). On finitely injective modules. J. Austral. Math. Soc. 16:239-248.
20. Sanh, N. V., Shum, K. P. (2001). Endomorphism rings of quasi-principally injective modules. Comm. Algebra 29:1437-1443.
21. Sanh, N. V., Shum, K. P., Dhompongsa, S., Wongwai, S. (1999). On quasi-principally injective modules. Algebra Colloq. 6:269-276.
22. Stenström, B. (1975). Rings of Quotients. Berlin: Springer-Verlag.
23. Wisbauer, R. (1991). Foundations of Module and Ring Theory. Philadelphia: Gordon and Breach Science Publishers.
24. Zhang, X. X., Chen, J. L. (2005). Homological properties characterized by matrices. J. Southeast Univ. (English Edition) 21:239-243.
25. Zhang, X. X., Chen, J. L., Zhang, J. (2005). On (m, n)-injective modules and (m, n)-coherent rings. Algebra Colloq. 12:149-160.
26. Zhu, S. L. (1991). On rings over which every flat left module is finitely projective. J. Algebra 139:311-321.
27. Zhu, Z. M., Chen, J. L., Zhang, X. X. (2005). On (m, n)-quasi-injective modules. Acta Math. Univ. Comenianae 124:25-36.
28. Zhu, Z. M., Chen, J. L., Zhang, X. X. (2004). On quasi-(m, n)-injective modules. Southeast Asian Bull. Math. 28:971-978.
29. Zhu, Z. M., Tan, Z. S. (2005). Minimal quasi-injective modules. Scientiae Math. Japon. 62(3):521-525.
30. Zimmermann, W. (1997). Modules with chain conditions for finite matrix subgroups. J. Algebra 190:68-87.