Soft representation of soft groups

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

Kaynakça

1. D. Molodtsov,”Soft set theory—first results.” Computers & Mathematics with Applications 37.4 (1999): 19-31.
2. P. K. Maji, R. Biswas and A.R. Roy, ”Soft set theory.” Computers & Mathematics with Applications 45.4 (2003): 555-562.
3. H. Aktas¸ and N. C¸ a˘gman, ”Soft sets and soft groups.” Information Sciences 177.13 (2007): 2726-2735.
4. J. B. Young “Soft BCK/BCI-algebras.” Computers & Mathematics with Applications 56.5 (2008): 1408-1413.
5. F. Feng, Y. B. Jun, and X. Zhao. ”Soft semirings.”Computers & Mathematics with Applications 56.10 (2008): 2621-2628.
6. 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.
7. U. Acar, F. Koyuncu, and B. Tanay. ”Soft sets and soft rings. ”Computers & Mathematics with Applications,59 (11) (2010):3458-3463.
8. Aktas¸, Hacı. ”Some algebraic applications of soft sets.” Applied Soft Computing 28 (2015): 327-331.

9. Aktas¸, Hacı, and S¸ erif O¨ zlu¨. ”Cyclic Soft Groups and Their Applications on Groups.” The Scientific World Journal 2014 (2014).
10. Sezer, A. S., Atag¨un, A. O., &Cagman, N. (2015). Uni-soft Substructures of Rings and Modules. Information Sciences Letters,4(1),7.
11. Jun, Y. B., &Song, S. Z. (2015). Int -Soft (Generalized) Bi-Ideals of Semigroups. The Scientific World Journal,2015.
12. S¸ ahin, M. Olgun, N. Kargın, A. and Uluc¸ay, V. (2015). Soft G-module, ICSCCW-2015.
13. Q. Sun, Z. Zang, and J. Liu, Soft sets and soft modules, Lecture Notes in Computer, Sci, 5009 (2008) 403 – 409.
14. C. W. Curties, Representation theory of finite group and associative algebra. Inc, (1962).
15. S. Nazmul and S. K. Samanta, Soft Topological soft group, Mathematical Sciences, (2012) 6:66.