A NOTE ON SOFT MODULES

In this paper, essential soft submodule and complement of a softsubmodule in a soft module are defined. The basic properties of such softsubmodules are obtained. The notion of complement of soft submodules onsoft modules is introduced. The relations between this and direct summand ofsoft modules are investigated

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  • Molodtsov, D., Soft Set Theory-First Results, Comput. Math. Appl. 37 (1999), 19-31.
  • Jun, Y.B., Soft BCK/BCI-algebra, Comput. Math. Appl. 56 (2008), 1408-1413.
  • Jun, Y.B. and Park, C.H., Application of soft sets in ideal theory of BCK-algebra, Information Sciences, 178 (2008), 2466-2475.
  • Maji, P.K., Biswas, R. and Roy, A.R., Soft Set Theory, Comput. Math. Appl. 45 (2003), 562.
  • Ali, M.I., Feng, F., Liu, X., Min, W.K. and Shabir, M., On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553.
  • Sezgin, A. and Atagün, A.O., On operations of soft sets, Comput. Math. Appl. 61 (2011), 1467.
  • Ali, M.I., Shabir, M. and Naz, M., Algebraic structures of soft sets associated with new operations, Comput. Math. Appl. 61 (2011), 2647-2654.
  • Aktas, H. and Çaµgman, N., Soft sets and soft groups, Information Sciences, 177 (2007), 2735.
  • Acar, U., Koyuncu, F. and Tanay, B., Soft sets and soft rings. Comput. Math. Appl. 59 (2010), 3458-3463.
  • Sun, Q.M., Zhang, Z.L. and Liu, J., Soft sets and soft modules, Lecture Notes in Comput. Sci. 5009 (2008), 403-409.
  • Atagün, A.O. and Sezgin, A., Soft substructures of rings, …elds and modules, Comput. Math. Appl. 61 (3)(2011), 592-601.
  • Türkmen, E. and Pancar, A., On some new operations in soft module theory, Neural Comput. and Appl. 22 (2013), 1233-1237.
  • Dung, N.V., Huynh, D.V., Smith, P.F. and Wisbauer, R., Extending Modules, Longman Scienti…c and Technical, New York, 1994.