A characterization of noetherian rings by cyclic modules

Proceedings of the Edinburgh Mathematical Society

Volumn 39, Issue 2, 1996, Pages 253-262

  Van Huynh, Dinh ^a  

^a Institute of Mathematics   (Viet Nam)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010537094     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0013091500022987     Document Type: Article

References (20)

1. F. W. ANDERSON and K. R. FULLER, Rings and Categories of Modules (Springer-Verlag 1974).
2. A. K. BOYLE and K. R. GOODEARL, Rings over which certain modules are injective, Pacific J. Math. 58(1975), 43-53.
3. A. W. CHATTERS, A characterization of right noetherian rings, Quart. J. Math. Oxford (2) 33 (1982), 65-69.
4. A. W. CHATTERS and C. R. HAJARNAVIS, Rings with Chain Conditions (Pitman, London 1980).
5. J. H. COZZENS, Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76(1970), 75-79.
6. R. F. DAMIANO, A right PCI ring is right noetherian, Proc. Amer. Math. Soc. 77 (1979), 11-14.
7. DINH VAN HUYNH and NGUYEN V. DUNG, A characterization of artinian rings, Glasgow Math. 7.30(1988), 67-73.
8. DINH VAN HUYNH and P. F. SMITH, Some rings characterised by their modules, Comm. Algebra (6)18(1990), 1971-1988.
9. DINH VAN HUYNH, NGUYEN V. DUNG and P. F. SMITH, A characterization of rings with Krull dimension, J. Algebra 132 (1990), 104-112.
10. DINH VAN HUYNH, NGUYEN V. DUNG and R. WISBAUER, On modules with finite uniform and Krull dimension, Arch. Math. 57 (1991), 122-132.
11. C. FAITH, When are proper cyclics injective?, Pacific J. Math. 45 (1973), 97-112.
12. C. FAITH, Algebra II: Ring Theory (Springer-Verlag 1976).
13. V. K. GOEL, S. K. JAIN and S. SINGH, Rings whose cyclic modules are injective or projective, Proc. Amer. Math. Soc. 53 (1975), 16-18.
14. R. GORDON and J. C. ROBSON, Krull dimension (Mem. Amer. Math. Soc. 123, 1973).
15. F. KASCH, Moduln und Ringe (Teubner, Stuttgart 1977).
16. A. KERTèSZ (Editor), Associative Rings, Modules and Radicals, in Proc. Colloquium at Keszthely in 1971 (J. Bolyai Math. Soc. North-Holland Publ. Co., Amsterdam-London-Budapest, 1973).
17. B. L. OSOFSKY and P. F. SMITH, Cyclic modules whose quotients have complements direct summands, J. Algebra 139 (1991), 342-354.
18. P. F. SMITH, Rings characterized by their cyclic modules, Canad. J. Math. 24 (1979), 93-111.
19. P. F. SMITH, DINH VAN HUYNH and NGUYEN V. DUNG, A characterization of noetherian modules, Quart. J. Math. Oxford 41 (1990), 225-235.
20. R. WISBAUER, Foundations of Module and Ring Theory (Gordon and Breach, Reading 1991).