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Soft representation of soft groups

Year 2016, Volume: 4 Issue: 2, 23 - 29, 01.03.2016

Vakkas Ulucay

Abstract

In this paper, we introduce the notion of soft representation of a soft group and obtain basic properties of soft representation of soft groups using the definition of soft sets and soft group. Also we study the relationship between soft representation of soft groups and soft G-Modules. Moreover we examine irreducibility, reducibility and complete reducibility of soft representations.

Keywords

Soft set soft group soft representation

References

  • D. Molodtsov,”Soft set theory—first results.” Computers & Mathematics with Applications 37.4 (1999): 19-31.
  • P. K. Maji, R. Biswas and A.R. Roy, ”Soft set theory.” Computers & Mathematics with Applications 45.4 (2003): 555-562.
  • H. Aktas¸ and N. C¸ a˘gman, ”Soft sets and soft groups.” Information Sciences 177.13 (2007): 2726-2735.
  • J. B. Young “Soft BCK/BCI-algebras.” Computers & Mathematics with Applications 56.5 (2008): 1408-1413.
  • F. Feng, Y. B. Jun, and X. Zhao. ”Soft semirings.”Computers & Mathematics with Applications 56.10 (2008): 2621-2628.
  • SUN, Qiu-Mei; ZHANG, Zi-Long; LIU, Jing. Soft sets and soft modules. In: Rough Sets and Knowledge Technology. Springer Berlin Heidelberg, 2008. p.403-409.
  • U. Acar, F. Koyuncu, and B. Tanay. ”Soft sets and soft rings. ”Computers & Mathematics with Applications,59 (11) (2010):3458-3463.
  • Aktas¸, Hacı. ”Some algebraic applications of soft sets.” Applied Soft Computing 28 (2015): 327-331.
  • Aktas¸, Hacı, and S¸ erif O¨ zlu¨. ”Cyclic Soft Groups and Their Applications on Groups.” The Scientific World Journal 2014 (2014).
  • Sezer, A. S., Atag¨un, A. O., &Cagman, N. (2015). Uni-soft Substructures of Rings and Modules. Information Sciences Letters,4(1),7.
  • Jun, Y. B., &Song, S. Z. (2015). Int -Soft (Generalized) Bi-Ideals of Semigroups. The Scientific World Journal,2015.
  • S¸ ahin, M. Olgun, N. Kargın, A. and Uluc¸ay, V. (2015). Soft G-module, ICSCCW-2015.
  • Q. Sun, Z. Zang, and J. Liu, Soft sets and soft modules, Lecture Notes in Computer, Sci, 5009 (2008) 403 – 409.
  • C. W. Curties, Representation theory of finite group and associative algebra. Inc, (1962).
  • S. Nazmul and S. K. Samanta, Soft Topological soft group, Mathematical Sciences, (2012) 6:66.

Year 2016, Volume: 4 Issue: 2, 23 - 29, 01.03.2016

Vakkas Ulucay

Abstract

References

  • D. Molodtsov,”Soft set theory—first results.” Computers & Mathematics with Applications 37.4 (1999): 19-31.
  • P. K. Maji, R. Biswas and A.R. Roy, ”Soft set theory.” Computers & Mathematics with Applications 45.4 (2003): 555-562.
  • H. Aktas¸ and N. C¸ a˘gman, ”Soft sets and soft groups.” Information Sciences 177.13 (2007): 2726-2735.
  • J. B. Young “Soft BCK/BCI-algebras.” Computers & Mathematics with Applications 56.5 (2008): 1408-1413.
  • F. Feng, Y. B. Jun, and X. Zhao. ”Soft semirings.”Computers & Mathematics with Applications 56.10 (2008): 2621-2628.
  • SUN, Qiu-Mei; ZHANG, Zi-Long; LIU, Jing. Soft sets and soft modules. In: Rough Sets and Knowledge Technology. Springer Berlin Heidelberg, 2008. p.403-409.
  • U. Acar, F. Koyuncu, and B. Tanay. ”Soft sets and soft rings. ”Computers & Mathematics with Applications,59 (11) (2010):3458-3463.
  • Aktas¸, Hacı. ”Some algebraic applications of soft sets.” Applied Soft Computing 28 (2015): 327-331.
  • Aktas¸, Hacı, and S¸ erif O¨ zlu¨. ”Cyclic Soft Groups and Their Applications on Groups.” The Scientific World Journal 2014 (2014).
  • Sezer, A. S., Atag¨un, A. O., &Cagman, N. (2015). Uni-soft Substructures of Rings and Modules. Information Sciences Letters,4(1),7.
  • Jun, Y. B., &Song, S. Z. (2015). Int -Soft (Generalized) Bi-Ideals of Semigroups. The Scientific World Journal,2015.
  • S¸ ahin, M. Olgun, N. Kargın, A. and Uluc¸ay, V. (2015). Soft G-module, ICSCCW-2015.
  • Q. Sun, Z. Zang, and J. Liu, Soft sets and soft modules, Lecture Notes in Computer, Sci, 5009 (2008) 403 – 409.
  • C. W. Curties, Representation theory of finite group and associative algebra. Inc, (1962).
  • S. Nazmul and S. K. Samanta, Soft Topological soft group, Mathematical Sciences, (2012) 6:66.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Vakkas Ulucay

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Ulucay, V. (2016). Soft representation of soft groups. New Trends in Mathematical Sciences, 4(2), 23-29.
AMA Ulucay V. Soft representation of soft groups. New Trends in Mathematical Sciences. March 2016;4(2):23-29.
Chicago Ulucay, Vakkas. “Soft Representation of Soft Groups”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 23-29.
EndNote Ulucay V (March 1, 2016) Soft representation of soft groups. New Trends in Mathematical Sciences 4 2 23–29.
IEEE V. Ulucay, “Soft representation of soft groups”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 23–29, 2016.
ISNAD Ulucay, Vakkas. “Soft Representation of Soft Groups”. New Trends in Mathematical Sciences 4/2 (March 2016), 23-29.
JAMA Ulucay V. Soft representation of soft groups. New Trends in Mathematical Sciences. 2016;4:23–29.
MLA Ulucay, Vakkas. “Soft Representation of Soft Groups”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 23-29.
Vancouver Ulucay V. Soft representation of soft groups. New Trends in Mathematical Sciences. 2016;4(2):23-9.
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