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Some aspects of quasi-pseudo principally injective modules. (English) Zbl 1425.16003

Summary: In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under direct summands. Several properties and characterizations have been given. In particular, we characterize Noetherian rings and Dedekind domains by quasi-pseudo principally injectivity.

MSC:

16D50 Injective modules, self-injective associative rings
16D10 General module theory in associative algebras
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References:

[1] M.S. Abbas and S.M. Saied, IC-pseudo-injective modules, International Journal of Algebra, 6(6) (2012) 255-264. · Zbl 1251.16003
[2] A. Barnard, Multiplication modules, J. Algebra, 71 (1981) 174-178. · Zbl 0468.13011
[3] Chang-woo Han and Su-Jeong Chol, Generalizations of the quasi-injective modules, Comm. Korean Math. Soc., 10(4) (1995) 811-813. · Zbl 0945.16005
[4] A. K. Chaturvedi, B. M. Pandeya and A. J. Gupta, Quasi-pseudo-principally injective modules, Algebra Colloq., 16(3) (2009) 397-402. · Zbl 1184.16003
[5] H. Q. Dinh, A note on pseudo-injective modules, Comm. Algebra, 33 (2005) 361-369. · Zbl 1077.16004
[6] A. Ghorbani and M. R. Vedadi, Epi-retractable modules and some applications, Bul. Iranian Math. Soc., 35(1) (2009) 155-166. · Zbl 1197.16005
[7] K. R. Goodearl, Ring theory, Nonsingular rings and modules, Marcel Dekker. Inc., New York (1976). · Zbl 0336.16001
[8] S. K. Jain and S. R. L´opez-Permouth, Weakly-injective modules over hereditary noetherian prime rings, J. Austral. Math. Soc. (Series A), 58 (1995) 287-297. · Zbl 0839.16003
[9] S. H. Mohamed and B. J. M¨uller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, Cambridge University Press, 14, (1990). · Zbl 0701.16001
[10] R. Y. C. Ming, On regular rings and self-injective rings, IV, Publications De l’institut Mathematique, Nouvelle serie tome, 45(59) (1989) 65-72. · Zbl 0685.16010
[11] V. S. Rodrigues and A. A. Sant’Ana, A note on a problem due to Zelmanowitz, Algebra and Discrete Mathematics, 3 (2009) 85-93. · Zbl 1199.16017
[12] J. J. Rotman, An introduction to homological algebra, Academic Press, New York, (2000). · Zbl 0441.18018
[13] N. V. Sanh, K. P. Shum, S. Dhompongsa and S. Wongwai, On quasi principally injective modules, Algebra Colloq., 6(3) (1999) 269-276. · Zbl 0949.16003
[14] S. Singh and S. K. Jain, On Pseudo-injective modules and self pseudo-injective rings, J. Math. Sci., 2 (1967) 23-31. · Zbl 0154.28301
[15] S. Baupradist, H. D. Hai and N. V. Sanh, On pseudo-p-injectivity, Southeast Asian Bull. Math., 35 (2011) 21-27. · Zbl 1240.16003
[16] M. K. Patel, B. M. Pandeya, A. J. Gupta and V. Kumar, Quasi principally injective modules, International Journal of Algebra, 4(26) (2010) 1255-1259. · Zbl 1242.16004
[17] R. Wisbauer, Foundations of module and ring theory, Revised and translated from the 1988 German edition, Algebra, Logic and Applications, Gordon and Breach Science Publishers, Philadelphia, PA, vol. 3 (1991). · Zbl 0746.16001
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