# THE ESSENCE OF SUBTRACTION ALGEBRAS BASED ON N-STRUCTURES

Lee, Kyoung-Ja;Jun, Young-Bae

• Published : 2012.01.31
• 29 10

#### Abstract

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-essence in a sub-traction algebra is introduced, and related properties are investigated. Relations among an $\mathcal{N}$-ideal, an $\mathcal{N}$-subalgebra and an $\mathcal{N}$-essence are investigated.

#### Keywords

subtraction algebra;N-subalgebra;N-ideal;N-essence

#### References

1. J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Inc., Boston, Mass. 1969.
2. Y. B. Jun, J. Kavikumar, and K. S. So, N-ideals of subtraction algebras, Commun. Korean Math. Soc. 25 (2010), no. 2, 173-184. https://doi.org/10.4134/CKMS.2010.25.2.173
3. Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. 65 (2007), no. 1, 129-134.
4. Y. B. Jun, H. S. Kim, and K. J. Lee, The essence of subtraction algebras, Sci. Math. Jpn. 64 (2006), no. 3, 601-606.
5. Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61 (2005), no. 3, 459-464.
6. Y. B. Jun, K. J. Lee, and S. Z. Song, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417-437.
7. Y. B. Jun, C. H. Park, and E. H. Roh, Order systems, ideals and right fixed maps of subtraction algebras, Commun. Korean Math. Soc. 23 (2008), no. 1, 1-10. https://doi.org/10.4134/CKMS.2008.23.1.001
8. B. M. Schein, Difference semigroups, Comm. Algebra 20 (1992), no. 8, 2153-2169. https://doi.org/10.1080/00927879208824453
9. B. Zelinka, Subtraction semigroups, Math. Bohem. 120 (1995), no. 4, 445-447.