Strongly $n$-Gorenstein projective, injective and flat modules
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Abstract
This paper generalize the idea of the authors in [3]. Namely, we define and study a particular case of modules with Gorenstein projective, injective, and flat dimension less or equal than n \geq 0 , which we call, respectively, strongly n-Gorenstein projective, injective and flat modules. These three classes of modules give us a new characterization of the first modules, and they are a generalization of the notions of strongly Gorenstein projective, injective, and flat modules respectively.
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Mahdou, N., & Tamekkante, M.
(2018).
Strongly $n$-Gorenstein projective, injective and flat modules.
Acta Mathematica Universitatis Comenianae, 87(1), 35-53.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/583/534
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References
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2. D. Bennis, A note on Gorenstein flat dimension, Algebra Colloquium 18 (2011),no. 1, 155–161.
3. D. Bennis and N. Mahdou; Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl. Algebra 210 (2007), 437-445.
4. D. Bennis and N. Mahdou; Global Gorenstein Dimensions, Proc. Amer. Math. Soc. 138(2) 368 (2010), 461–465.
5. D. Bennis and N. Mahdou; Global Gorenstein dimensions of polynomial rings and of direct products of rings, Houston J. Math. 25(4) (2009), 1019–1028
6. D. Bennis and N. Mahdou; A generalization of strongly Gorenstein projective modules, J. Algebra Appl. 8 (2009), 219-227.
7. N. Bourbaki, Alg`ebre Homologique, Chapitre 10, Masson, Paris, (1980).
8. L. W. Christensen; Gorenstein dimensions, Lecture Notes in Math., 1747, Springer, Berlin, (2000).
9. L. W. Christensen, A. Frankild, and H. Holm; On Gorenstein projective, injective and flat dimensions - a funcTorial description with applications, J. Algebra 302 (2006), 231-279.
10. E. E. Enochs and O. M. G. Jenda;Relative homological algebra, de Gruyter Expositions in Mathematics, vol. 30, Walter de Gruyter Co., Berlin, (2000).
11. E. Enochs and O. Jenda; On Gorenstein injective modules, Comm. Algebra 21 (1993), no. 10, 3489-3501.
12. E. Enochs and O. Jenda; Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633.
13. E. Enochs, O. Jenda and B. Torrecillas; Gorenstein flat modules, Nanjing Daxue Xuebao Shuxue Bannian Kan 10 (1993), no. 1, 1-9.
14. S. Glaz; Commutative Coherent Rings, Springer-Verlag, Lecture Notes in Mathematics, 13-71 (1989).
15. H. Holm; Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), 167-193.
16. I. Kaplansky; Commutative Rings, Allyn and Bacon, Boston, (1970).
17. N. Mahdou; On Costas conjecture, Comm. Algebra 29 (7) (2001) 2775-2785.
18. W. K. Nicholson and M. F. Youssif; Quasi-Frobenius Rings, Cambridge University Press, vol. 158, 2003.
19. J. Rotman; An Introduction to Homological Algebra, Academic press, Pure and Appl. Math, A Series of Monographs and Textbooks, 25 (1979).
20. C. A. Weibel; An Introduction to Homological Algebra, Cambridge University Press, Cambridge, Cambridge studies in advanced mathematics, 38 (1994).
21. G. Zhao and Z. Huang; n-strongly Gorenstein projective, injective and flat modules, Comm. Algebra 39 (2011), no. 8, 3044–3062.