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ON PSEUDO BH-ALGEBRAS
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  • Journal title : Honam Mathematical Journal
  • Volume 37, Issue 2,  2015, pp.207-219
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2015.37.2.207
 Title & Authors
ON PSEUDO BH-ALGEBRAS
JUN, YOUNG BAE; AHN, SUN SHIN;
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 Abstract
As a generalization of BH-algebras, the notion of pseudo BH-algebra is introduced, and some of their properties are investigated. The notions of pseudo ideals, pseudo atoms, pseudo strong ideals, and pseudo homomorphisms in pseudo BH-algebras are introduced. Characterizations of their properties are provided. We show that every pseudo homomorphic image and preimage of a pseudo ideal is also a pseudo ideal. Any pseudo ideal of a pseudo BH-algebra can be decomposed into the union of some sets. The notion of pseudo complicated BH-algebra is introduced and some related properties are obtained.
 Keywords
pseudo atom;pseudo (strong) ideal;pseudo (complicated) BH-algebra;
 Language
English
 Cited by
 References
1.
J. M. Font, A. J. Rodrgez and A. Torrens, Wajsbergs Algebras, Stochastica, 8(1984), 5-31.

2.
G. Georgescu and A. Iorgulescu, Pseudo BCK-algebras, in: Proc. DMTS'01: Combinatorics, Computability and Logics, Springer, London, 2001, 97-114.

3.
K. Iseki, On BCI-algebras, Math. Seminar Notes, 8(1980), 125-130.

4.
K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon., 23(1978), 1-26.

5.
Y. B. Jun, H. S. Kim and J. Neggers, On pseudo d-algebras, Inform. Sci., 179(2009), 1751-1759. crossref(new window)

6.
Y. B. Jun, Characterizations of pseudo BCK-algebras, Sci. Math. Japon. Online, 7(2002), 225-230.

7.
Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math. Japon., 1(1998), 347-354.

8.
J. Meng, Implicative commutative semigroups are equivalent to a class of BCK-algebras, Semigroup Forum, 50(1995), 89-96. crossref(new window)

9.
J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa, Seoul, 1994.

10.
D. Mundici, MV -algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japon., 31(1986), 889-894.

11.
E. H. Roh and S. Y. Kim, On BH*-subalgebras of transitive BH*-algebras, Far East J. Math. Sci., 1(1999), 255-263.