Ideal Theory of BE-Algebras Based on N-Structures  ABSTRACT  |  FULL TEXT

Year 2012, Volume: 41 Issue: 4, 435 - 447, 01.04.2012

Young Bae Jun  min Su Kang

Abstract

Using N-structures, the notion of an N-ideal in a BE-algebra is introduced. Characterizations of an N-ideal are discussed. Conditions for
an N-structure to be an N-ideal are provided. To obtain a more general form of an N-ideal, a point N-structure which is (conditionally)
employed in an N-structure is proposed. Using these notions, the concept of an ([e], [e]∨[c])-ideal is introduced, and related properties are
investigated. Characterizations of ([e], [e]∨[c])-ideals are discussed.

Keywords

(Transitive , Ideal , N-ideal , 2000 AMS Classification: 06 F 35

References

• Ahn, S. S. and So, K. S. On ideals and upper sets in BE-algerbas, Sci. Math. Japan 68, 279–285, 2008.
• Imai, Y. and Is´eki, K. On axiom systems of propositional calculi XIV, Proc. Japan Academy 42, 19–22, 1966.
• Is´eki, K. An algebra related with a propositional calculus, Proc. Japan Academy 42, 26–29, 1966.
• Jun, Y. B., Lee, K. J. and Song, S. Z. N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22, 417–437, 2009.
• Kim, H. S. and Kim, Y. H. On BE-algerbas, Sci. Math. Jpn. 66, 113–116, 2007.
• Molodtsov, D. Soft set theory - First results, Comput. Math. Appl. 37, 19–31, 1999.
• Song, S. Z., Jun, Y. B. and Lee, K. J. Fuzzy ideals in BE-algebras, Bull. Malays. Math. Sci. Soc. 33, 147–153, 2010.