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

Year 2012, Volume: 12 Issue: 12, 162 - 174, 01.12.2012

Driss Bennis Habib Bouzraa Abdul-qawe Kaed

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

• F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer- Verlag, Heidelberg, New York, 1974.
• D. Bennis, n-X -coherent rings, Int. Electron. J. Algebra, 7 (2010), 128–139.
• A. J. Berrick and M. E. Keating, An Introduction to Rings and Modules, Cambridge University Press 65, 2000.
• N. Bourbaki, Alg`ebre Commutative, Chapitres 1-4, Masson, Paris, 1985.
• J. Chen and X. Zhang, On n-Semihereditary and n-Coherent Rings, Int. Elec- tron. J. Algebra, 1 (2007), 1–10.
• J. L. Chen and N. Q. Ding, On n-coherent rings, Comm. Algebra, 24 (1996), –3216.
• D. L. Costa, Parameterizing families of non-Noetherian rings, Comm. Alge- bra, 22 (1994), 3997–4011.
• 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.
• 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.
• V. A. Hiremath, Cofinitely generated and cofinitely related modules, Acta Math. Hungar., 39 (1982), 1–9.
• S. Glaz, Commutative Coherent Rings, Lecture Notes in Math., Springer- Verlag, Berlin, 1989.
• J. P. Jans, On co-Noetherian rings, J. London Math. Soc., 1 (1969), 588–590.
• C. Jian-long and Z. Zhan-min, FCP-projective modules and some rings, J. Zhejiang Univ. Sci. Ed., 37 (2010), 126–130.
• J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.
• P. Vamos, The dual of the notion of “finitely generated”, J. London Math. Soc., 43 (1968), 643–646.
• R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991.
• W. M. Xue, On n-presented modules and almost excellent extensions, Comm. Algebra, 27 (1999), 1091–1102.
• D. X. Zhou, On n-coherent rings and (n,d)-rings, Comm. Algebra, 32 (2004), –2441. Driss Bennis
• Department of Mathematics Laboratory of Analysis, Algebra and Decision Support Faculty of Science, BP 1014,
• 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]