Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Characterizations of Several Modules Relative to the Class of B(M, X)

  • Talebi, Yahya (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran) ;
  • Hosseinpour, Mehrab (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran)
  • Received : 2011.03.01
  • Accepted : 2012.05.03
  • Published : 2013.03.23
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Abstract

Let M and X be right R-modules. We introduce several modules relative to the class of B(M, X) and we investigate relation among these modules. In this note, we show if M is X-${\oplus}$-supplemented such that $M=M_1{\oplus}M_2$ implies $M_1$ and $M_2$ are relatively B-projective, then M is an X-H-supplemented module.

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References

  1. N. Agayev, T. Kosan, A. Leghwel and A. Harmanci, Duo modules and duo rings, Far East J. Math. Sci., 20(3)(2006) 341-346.
  2. M. Alkan and A. Harmanci, On Summand Sum and Summand Intersection Property of Modules, Turkish J. Math., 26(2002) 131-147.
  3. C. Chang, X-lifting modules over right perfect rings, Bull. Korean Math. Soc., 45(1)(2008) 59-66. https://doi.org/10.4134/BKMS.2008.45.1.059
  4. J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkhauser, Basel-Boston- Berlin, (2006).
  5. J. L. Garcia, Properties of direct summands of modules, Comm. Algebra, 17(1)(1989), 73-92. https://doi.org/10.1080/00927878908823714
  6. J. Hausen, Modules with the summand intersection property, Comm. Algebra, 17(1)(1989), 135-148. https://doi.org/10.1080/00927878908823718
  7. A. Harmanci, D. Keskin and P.F. Smith, On $\oplus$-supplemented modules, Acta Math. Hungar., 83(1-2)(1999), 161-169. https://doi.org/10.1023/A:1006627906283
  8. D. Keskin and A. Harmanci, A relative version of the lifting property of modules, Algebra Colloq., 11(3)(2004), 361-370.
  9. M. T. Kosan, H-cofinitely supplemented modules, Vietnam J. Math., 35(2)(2007), 1-8.
  10. S. R. Lopez-Permouth, K. Oshiro and S. Tariq Rizvi, On the relative (quasi-) conti- nuity of modules, Comm. Algebra, 17(1998), 3497-3510.
  11. S. H. Mohammed and B. J. Muller, Continous and Discrete Modules, London Math. Soc., LN 147, Cambridge Univ. Press, (1990).
  12. N. Orhan and D. K. Tutuncu, Characterizations of lifting modules in terms of cojective modules and the class of B(M,X), Int. J. Math., 16(6)(2005), 647-660. https://doi.org/10.1142/S0129167X05003041
  13. Y. Talebi and T. Amoozegar, Strongly FI-lifting modules, Int. Electr. J. Algebra, 3(2008), 75-82.
  14. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, (1991).