A COUPLED 𝒩-STRUCTURE WITH AN APPLICATION IN A SUBTRACTION ALGEBRA

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 4,  2014, pp.863-884
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.4.863
Title & Authors
A COUPLED 𝒩-STRUCTURE WITH AN APPLICATION IN A SUBTRACTION ALGEBRA
Williams, D.R. Prince; Ahn, Sun Shin; Jun, Young Bae;

Abstract
In this paper, we introduce a coupled $\small{\mathcal{N}}$-structure which is the generalization of $\small{\mathcal{N}}$-structure. Using this coupled $\small{\mathcal{N}}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\small{\mathcal{N}}$-subalgebra, a coupled $\small{\mathcal{N}}$-ideal. Also the characterization of coupled $\small{\mathcal{N}}$-ideal is presented.
Keywords
$\small{\mathcal{N}}$-subalgebras;$\small{\mathcal{N}}$-ideals;coupled $\small{\mathcal{N}}$-subalgebras;coupled $\small{\mathcal{N}}$-ideals;
Language
English
Cited by
References
1.
J. C. Abbott, Sets, Lattices and Boolean Algebra, Allyn and Bacon, Boston, 1969.

2.
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 1 (1986), 87-96.

3.
K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems. 61 (1994), 137-142.

4.
Y. Ceven and M. A Ozturk, Some results on subtraction algebras, Hacettepe Journal of Mathematics and Statistics 38 (2009), 299-304.

5.
Y. B. Jun, H. S. Kim and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61 (2005), 459-464.

6.
Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. 65 (2007), 129-134.

7.
Y. B. Jun, K. J. Lee and S. Z. Song, $\aleph$-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417-437.

8.
Y. B. Jun, J. Kavikumar and K. S. So, N-ideals of subtraction algebras, Commun. Korean Math. Soc. 25 (2010), 173-184.

9.
A. Khan, Y. B. Jun and M. Shabir, N-fuzzy ideals in ordered semigroups, International Journal of Mathematics and Mathematical Sciences. 1 (2009), 1-4.

10.
Y. B. Jun, S. S. Ahn and D. R. Prince Williams, Coupled N-structures and its application in BCK/BCI-algebras, (in press).

11.
A. Khan, Y. B. Jun and M. Shabir, N-fuzzy filters in ordered semigroups, Mohu Xitong yu Shuxue 24 (2010), 28-32.

12.
K. J. Lee and C. H. Park, Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22 (2007), 359-363.

13.
B. M. Schein, Difference Semigroups, Comm. Algebra 20 (1992), 2153-2169.

14.
L. A. Zadeh, Fuzzy sets, Information Control 8 (1965), 338-353.

15.
L. A. Zelinka, Subtraction semigroup, Math. Bohemica 120 (1995), 445-447.