Skip to main content
Log in

On Q-Upper Algebras

  • Published:
Order Aims and scope Submit manuscript

Abstract

Given a poset we introduce the notion of Q-upper algebras and study the (positive) implicativity, commutativity and quasi-commutativity in Q-upper algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Birkhoff, G. and von Neumann, J.: The logic of quantum mechanics, Ann. Math. 37 (1936), 823–834.

    Article  MathSciNet  Google Scholar 

  2. Chaudhary, M. A. and Ahmad, B.: On a class of BCI-algebras, Math. Jpn. 33(6) (1988), 827–830.

    MathSciNet  MATH  Google Scholar 

  3. Dudek, W. A.: On some BCI-algebras with the condition (S), Math. Jpn. 31(1) (1986), 25–29.

    MathSciNet  MATH  Google Scholar 

  4. Dvurečenskij, A.: Commutative BCK-algebras and quantum structures, Int. J. Theor. Phys. 39(3) (2000), 653–664.

    MATH  Google Scholar 

  5. Dvurečenskij, A. and Graciano, M. G.: Dedekind complete commutative BCK-algebras, Order 17 (2000), 23–41.

    Article  MathSciNet  MATH  Google Scholar 

  6. Dvurečenskij, A. and Kim, H. S.: Connections between BCK-algebras and difference posets, Stud. Log. 60 (1998), 421–439.

    Article  MATH  Google Scholar 

  7. Greechie, R. J. and Foulis, D. J.: Transition to effect algebras, Int. J. Theor. Phys. 34 (1995), 1369–1382.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hong, S. M., Jun, Y. B. and Roh, E. H.: k-nil radical in BCI-algebras, Far East J. Math. Sci. 5 (1997), 237–242.

    MathSciNet  MATH  Google Scholar 

  9. Hoo, C. S.: MV and BCK-algebras on posets, Math. Jpn. 36 (1991), 137–141.

    MathSciNet  MATH  Google Scholar 

  10. Imai, Y. and Iséki, K.: On axiom systems of propositional calculi, Proc. Jpn. Acad. 42 (1966), 19–21.

    Article  MATH  Google Scholar 

  11. Iséki, K.: Remarks on BCK-algebras, Math. Semin. Notes 3 (1975), 45–54.

    Google Scholar 

  12. Iséki, K.: Some problems on BCK-algebras, Math. Semin. Notes 8 (1980), 395–402.

    MATH  Google Scholar 

  13. Iséki, K. and Tanaka, S.: An introduction to theory of BCK-algebras, Math. Jpn. 23 (1978), 1–26.

    MATH  Google Scholar 

  14. Jun, Y. B. and Xin, X. L.: On p-semisimple BCI-algebras and pomonoids, Soochow J. Math. 24(2) (1998), 131–140.

    MathSciNet  MATH  Google Scholar 

  15. Kim, J. Y., Jun, Y. B. and Kim, H. S.: BCK-algebras inherited from the posets, Math. Jpn. 45 (1997), 119–123.

    MathSciNet  MATH  Google Scholar 

  16. Kôpka, F. and Chovance, F.: D-posets, Math. Slovaca 44 (1994), 21–34.

    MathSciNet  MATH  Google Scholar 

  17. Meng, J. and Jun, Y. B.: BCK-Algebras, Kyung Moon Sa Co., Korea, 1994.

    MATH  Google Scholar 

  18. Neggers, J. and Kim, H. S.: Basic Posets, World Scientific Pub. Co., Singapore, 1998.

    MATH  Google Scholar 

  19. Setō, Y.: Some examples of BCK-algebras, Math. Semin. Notes 5 (1977), 397–400.

    MATH  Google Scholar 

  20. Tanaka, S.: A new class of algebras, Math. Semin. Notes 3 (1975), 37–43.

    Google Scholar 

  21. Tanaka, S.: Examples of BCK-algebras, Math. Semin. Notes 3 (1975), 75–82.

    Google Scholar 

  22. Yutani, H.: Quasi-commutative BCK-algebras and congruences relations, Math. Semin. Notes 5 (1977), 469–481.

    MathSciNet  MATH  Google Scholar 

  23. Yutani, H.: Reduction of types of quasi-commutative BCK-algebras, Math. Jpn. 6 (1990), 1065–1068.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hee Sik Kim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jun, Y.B., Kim, J.Y. & Kim, H.S. On Q-Upper Algebras. Order 22, 191–200 (2005). https://doi.org/10.1007/s11083-005-9010-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-005-9010-0

Mathematics Subject Classification (2000)

Key Words

Navigation