Some Soft Algebraic Structures
Abstract
Soft set theory was initiated by Molodtsov [9]. Then, Maji et al [8] defined some operations on soft sets. Akta¸s and C¸ aˇgman [2] defined soft groups and examined some related properties. Feng et al. [5] defined soft semirings. Acar et al. [1] defined soft rings and studied some of their properties In this study, we have defined soft fields and introduced some of their properties. Moreover, we have defined some kinds of ideals of soft rings and soft quotient rings.
Keywords
Soft sets,Soft rings,Soft fields,Soft ideals,Soft quotient rings
References
- Acar U., Koyuncu F., Tanay B., Soft sets and soft rings, Comput. Math. Appl. 59 (2010) 3458-3463.
- Aktas H., C¸ a˘gman N., Soft sets and soft groups, Inform. Sci. 177 (2007) 2726-2735.
- Ali M. Irfan, Feng F., Liu Xiaoyan, Minc Won Keun, Shabir M., On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547-1553.
- K. V. Babitha, J. J. Sunil, Soft set relations and functions, Comput. and Math. with Appl. 60 (2010) 1840-1849.
- Feng F., Jun Y. B., Zhao X., Soft semirings, Comput. Math. Appl. 56 (2008) 2621-2628.
- Hungerford Thomas W., Algebra, 1974, Springer-Verlag New York Inc.
- Jun Y. B., Soft BCK/BCI-algebra, Comput. Math. Appl. 56 (2008) 1408-1413.
- Maji P. K., Biswas R., Roy A. R. , Soft set theory, Comput. Math. Appl. 45 (2003) 555-562.
- Molodtsov D., Soft set theory-first result, Comput. Math. Appl. 37 (1999) 19-31.
- Sun Qiu-Mei, Zhang Zi-Liong, Liu Jing, Soft sets and soft modules, Lecture Notes in Comput. Sci. 5009 (2008) 403-409.