International Journal of Modern Science and Technology

INDEXED IN 

ISSN 2456-0235

​International Journal of Modern Science and Technology, 1(8), 2016, Pages 276-282. 


Cubic Ideals in Near Subtraction Semigroups 

V. Chinnadurai, K. Bharathivelan
Department of Mathematics, Annamalai University, Chidambaram,Tamilnadu - 608 002. India.

Abstract
Fuzzy set theory plays a significant role in mathematics. The study of algebra in fuzzy setting has always attracted researchers to a greater extend. Young Bae Jun made effort in defining a remarkable structure namely cubic structure and ideal theory in subtraction algebra. Concept of cubic sets encompasses interval-valued fuzzy set and fuzzy set. Interval-valued fuzzy set is another generalization of fuzzy sets that was introduced by Lotfi Asker Zadeh. Dheena introduced near-subtraction semigroups in fuzzy algebra. Motivated by the theory of cubic structure and near-subtraction semigroups. Our aim in this paper is to introduce the notion of cubic ideals of near-subtraction semigroups, homomorphism of near-subtraction semigroups and family of cubic ideals in intersection. We also provide some results, examples and study their related properties.

​​Keywords: Semigroups; Subtraction semigroups; Near-subtraction semigroups; Cubic ideal. 

​References

  1. Abbott JC. Sets, Lattices and boolean algebra. Allyn and Bacon, Boston. 1969.
  2. Schein BM. Difference semigroups. Communications in Algebra.  1992;8:2153-2169.
  3. Zelinka B. Subtraction semigroups. Mathematica Bohemica. 1995;8:445-447.
  4. Jun YB,   Kim HS. On ideals  in subtraction algebra. Scientiae Mathematicae Japonicae. 2007;65:129-134.
  5. Lee KJ, Park CH. Some questions on fuzzifications of ideals in subtraction algebras. Commun. Korean. Math. Soc. 2007;22:359-363.
  6. Zekiye Ciloglu, Yilmaz Ceven. On fuzzy ideals of subtraction semigroups. SDU Journal of Science (E-Journal). 2014;9:193-202.
  7. Dheena P,   Sateesh kumar G. On strongly regular near subtraction semigroups. Communication of Korean Mathematical Society. 2007;22:323-330.
  8. Lekkoksung S. On fuzzy ideals in near-subtraction ordered semigroups. Int. Jour. Contemp. Math. Sciences. 2012;7:1199-1204.
  9. Jun YB,  Kim CS, Yang KO. Cubic sets. Annals of Fuzzy Mathematics and Informatics. 2012;4:83-98.
  10. Jun YB, Jung ST, Kim MS. Cubic subgroups. Annals of Fuzzy Mathematics and Informatics. 2011;2: 9 -15.
  11. Vijayabalaji S, Sivaramakrishnan S. A Cubic set theoretical approach to linear space. Abstract and Applied Analysis. 2015.
  12. Chinnadurai V, Bharathivelan K. Cubic ideals of -semigroups. International Journal of Current Research and Modern Education. 2016;1:138-150.
  13. Chinnadurai V, Bharathivelan K, Vijayabalaji S, Sivaramakrishnan S. Cubic ring. Global Journal of Pure and Applied Mathematics. 2016;12:947-950.
  14. Zadeh LA. Fuzzy sets. Information and Computation. 1965;8:338-353.
  15. Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning I. Information Sciences. 1975;8:1-24.
  16. Jun YB,  Kim CS, Kang MS. Cubic subalgebras and ideals of BCK/BCI – algebras. Far East Journal of Mathematical Science.  2010;44:239 -250.
  17. Prince Williams DR. Fuzzy ideals in near-subtraction semigroups. International Scholarly and Scientific Research & Innovation. 2008;2:458-468.
  18. Chinnadurai V. Fuzzy ideals in algebraic structures. Germany: Lap Lambert Academic Publishing; 2013.