DOI QR코드

DOI QR Code

CONSTRUCTION OF MANY d-ALGEBRAS

Allen, Paul J.

  • 발행 : 2009.07.31

초록

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

키워드

BCK/d-algebra;constructive functions;commutative;BCK-point;transitivity set

참고문헌

  1. Q. P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983), 313–320
  2. Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japonica 30 (1985), 659–661
  3. K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125–130
  4. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica 23 (1978), 1–26
  5. Y. B. Jun, J. Neggers, and H. S. Kim, Fuzzy d-ideals of d-algebras, J. Fuzzy Math. 8 (2000), 123–130
  6. Y. C. Lee and H. S. Kim, On d-subalgebras of d-transitive $d^*$-algebras, Math. Slovaca 49 (1999), 27–33
  7. J. Meng, Implicative commutative semigroups are equivalent to a class of BCK-algebras, Semigroup Forum 50 (1995), 89–96 https://doi.org/10.1007/BF02573506
  8. J. Meng and Y. B. Jun, BCK-Algebras, Kyung Moon Sa, Seoul, 1994
  9. D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCKalgebras, Math. Japonica 31 (1986), 889–894
  10. J. Neggers, Y. B. Jun, and H. S. Kim, On d-ideals in d-algebras, Math. Slovaca 49 (1999), 243–251
  11. P. J. Allen, H. S. Kim, and J. Neggers, On companion d-algebras, Math. Slovaca 57 (2007), 93–106 https://doi.org/10.2478/s12175-007-0001-z
  12. J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), 19–26