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A NOTE ON SOFT MODULES

Year 2017, Volume: 66 Issue: 1, 66 - 74, 01.02.2017
https://doi.org/10.1501/Commua1_0000000775

Abstract

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

References

  • 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.
Year 2017, Volume: 66 Issue: 1, 66 - 74, 01.02.2017
https://doi.org/10.1501/Commua1_0000000775

Abstract

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Canan Celep Yücel This is me

Ummahan Acar This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Celep Yücel, C., & Acar, U. (2017). A NOTE ON SOFT MODULES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 66-74. https://doi.org/10.1501/Commua1_0000000775
AMA Celep Yücel C, Acar U. A NOTE ON SOFT MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):66-74. doi:10.1501/Commua1_0000000775
Chicago Celep Yücel, Canan, and Ummahan Acar. “A NOTE ON SOFT MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 66-74. https://doi.org/10.1501/Commua1_0000000775.
EndNote Celep Yücel C, Acar U (February 1, 2017) A NOTE ON SOFT MODULES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 66–74.
IEEE C. Celep Yücel and U. Acar, “A NOTE ON SOFT MODULES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 66–74, 2017, doi: 10.1501/Commua1_0000000775.
ISNAD Celep Yücel, Canan - Acar, Ummahan. “A NOTE ON SOFT MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 66-74. https://doi.org/10.1501/Commua1_0000000775.
JAMA Celep Yücel C, Acar U. A NOTE ON SOFT MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:66–74.
MLA Celep Yücel, Canan and Ummahan Acar. “A NOTE ON SOFT MODULES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 66-74, doi:10.1501/Commua1_0000000775.
Vancouver Celep Yücel C, Acar U. A NOTE ON SOFT MODULES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):66-74.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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