ON n-COPRESENTED MODULES AND n-CO-COHERENT RINGS

Abstract

In this paper, we introduce and study dual notions of both npresented modules and n-coherent rings, which we call respectively n-copresented modules and n-co-coherent rings.

Keywords

• finitely embedded modules, finitely cogenerated modules, n-presented modules, n-copresented modules, Noetherian rings, co-Noetherian rings, coherent rings, co-coherent rings, n-coherent rings, n-co-coherent rings

References

1. F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer- Verlag, Heidelberg, New York, 1974.
2. D. Bennis, n-X -coherent rings, Int. Electron. J. Algebra, 7 (2010), 128–139.
3. A. J. Berrick and M. E. Keating, An Introduction to Rings and Modules, Cambridge University Press 65, 2000.
4. N. Bourbaki, Alg`ebre Commutative, Chapitres 1-4, Masson, Paris, 1985.
5. J. Chen and X. Zhang, On n-Semihereditary and n-Coherent Rings, Int. Elec- tron. J. Algebra, 1 (2007), 1–10.
6. J. L. Chen and N. Q. Ding, On n-coherent rings, Comm. Algebra, 24 (1996), –3216.
7. D. L. Costa, Parameterizing families of non-Noetherian rings, Comm. Alge- bra, 22 (1994), 3997–4011.
8. D. E. Dobbs, S. Kabbaj and N. Mahdou, n-coherent rings and modules, Lec- ture Notes in Pure and Appl. Math., Dekker, 185 (1997), 269–281.

9. D. E. Dobbs, S. Kabbaj, N. Mahdou and M. Sobrani, When is D + M n-coherent and an (n, d)-domain?, Lecture Notes in Pure and Appl. Math., Dekker, 205 (1999), 257–270.
10. V. A. Hiremath, Cofinitely generated and cofinitely related modules, Acta Math. Hungar., 39 (1982), 1–9.
11. S. Glaz, Commutative Coherent Rings, Lecture Notes in Math., Springer- Verlag, Berlin, 1989.
12. J. P. Jans, On co-Noetherian rings, J. London Math. Soc., 1 (1969), 588–590.
13. C. Jian-long and Z. Zhan-min, FCP-projective modules and some rings, J. Zhejiang Univ. Sci. Ed., 37 (2010), 126–130.
14. J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.
15. P. Vamos, The dual of the notion of “finitely generated”, J. London Math. Soc., 43 (1968), 643–646.
16. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991.
17. W. M. Xue, On n-presented modules and almost excellent extensions, Comm. Algebra, 27 (1999), 1091–1102.
18. D. X. Zhou, On n-coherent rings and (n,d)-rings, Comm. Algebra, 32 (2004), –2441. Driss Bennis
19. Department of Mathematics Laboratory of Analysis, Algebra and Decision Support Faculty of Science, BP 1014,
20. Mohammed V-Agdal University, Rabat, Morocco e-mail: [e-mail]; driss [e-mail] Habib Bouzraa Department of Mathematics Faculty of Science University Mouly Ismail Meknes, Morocco e-mail: [e-mail] Abdul-Qawe Kaed Department of Mathematics Faculty of Science University Mouly Ismail Meknes, Morocco e-mail: [e-mail]