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In this paper, we provide some characterizations of semisimple rings, right V-rings, right hereditary and regular right FGC-rings in terms of C3-modules. The notions of C3-envelope and C3-cover are introduced.
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Czasopismo
Rocznik
Tom
Strony
282--292
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics University of Guilan P.O. BOX 1914, Rasht, Iran
autor
- Department of Mathematics University of Guilan P.O. BOX 1914, Rasht, Iran
autor
- Department of Mathematics University of Guilan P.O. BOX 1914, Rasht, Iran
Bibliografia
- [1] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, 2nd ed, New York, Springer-Verlag, 1992.
- [2] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488.
- [3] M. Behboodi, G. Behboodi Eskandari, On rings each of whose finitely generated modules is a direct sum of cyclic modules, arXiv preprint, arXiv:1202.0386, 2012.
- [4] K. A. Byrd, Rings whose quasi-injective modules are injective, Proc. Amer. Math. Soc. 33 (1972), 235–240.
- [5] J. L. Chen, W. X. Li, On artiness of right CF rings, Comm. Algebra 32 (2004), 4485–4494.
- [6] E. E. Enochs, O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expositions in Mathematics, 30, Walter de Gruyter co., Berlin, 2000.
- [7] J. L. Garcia, Properties of direct summands of modules, Comm. Algebra 17 (1989), 73–92.
- [8] A. Hamdouni, A. Ç. Özcan, A. Harmanci, Characterization of modules and rings by the summand intersection property and the summand sum property, JP J. Algebra Number Theory Appl. 5 (2005), 469–490.
- [9] A. Harmanci, P. F. Smith, A. Tercan, Y. Tiras, The Bass-Papp theorem and some related result, Vietnam J. Math. 25 (1997), 33–39.
- [10] J. Hausen, Modules with the summand intersection property, Comm. Algebra 17 (1989), 135–148.
- [11] F. Kourki, When maximal linearly independent subsets of a free module have the same cardinality?, Modules and Comodules, Trends in Mathematics, Birkhäuser Verlag, Basel, 281–293, 2008.
- [12] T. Y. Lam, Lectures on Modules and Rings, New York, Springer-Verlag, 1998.
- [13] G. Lee, S. T. Rizvi, C. S. Roman, Direct sums of Rickart modules, J. Algebra 353 (2012), 62–78.
- [14] G. Lee, S. T. Rizvi, C. S. Roman, Dual Rickart modules, Comm. Algebra 39 (2011), 4036–4058.
- [15] S. H. Mohamed, B. J. Müller, Continuous and Discrete Modules, Cambridge, UK, Cambridge Univ. Press, 1990.
- [16] W. K. Nicholson, M. F. Yousif, On perfect simple-injective rings, Proc. Amer. Math. Soc. 125 (1997), 979–985.
- [17] W. K. Nicholson, M. F. Yousif, Quasi-Frobenius Rings, Cambridge Tracts in Mathematics 158, Cambridge University Press, 2003.
- [18] R. S. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc. 70 (1967).
- [19] L. Shen, J. Chen, On countably-C2 rings, arXiv preprint, arXiv:1005.4167, 2010.
- [20] Y. Utumi, On continuous rings and selfinjective rings, Trans. Amer. Math. Soc. 118 (1965), 158–173.
- [21] R. Wisbauer, Foundations of Module and Ring Theory, Philadelphia: Gordon and Breach, 1991.
- [22] M. Yousif, I. Amin, Y. Ibrahim, D3-modules, Comm. Algebra 42 (2014), 578–592.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
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Bibliografia
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