DOI QR코드

DOI QR Code

ORDER SYSTEMS, IDEALS AND RIGHT FIXED MAPS OF SUBTRACTION ALGEBRAS

  • Jun, Young-Bae (DEPARTMENT OF MATHEMATICS EDUCATION (AND RINS) GYEONGSANG NATIONAL UNIVERSITY) ;
  • Park, Chul-Hwan (DEPARTMENT OF MATHEMATICS UNIVERSITY OF ULSAN) ;
  • Roh, Eun-Hwan (DEPARTMENT OF MATHEMATICS EDUCATION CHINJU NATIONAL UNIVERSITY OF EDUCATION)
  • Published : 2008.01.31

Abstract

Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.

Keywords

References

  1. J. C. Abbott, Semi-Boolean algebras, Matemat. Vesnik 4 (1967), 177-198
  2. J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston 1969
  3. S. S. Ahn, Y. H. Kim, and K. J. Lee, A relation on subtraction algebras, Sci. Math. Jpn. Online e-2005 (2005), 51-55
  4. G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ., Vol. 25, second edition 1984; third edition, 1967, Providence
  5. G. Gratzer, Universal Algebra, 2nd edition, Springer-Verlag, New York Inc., 1979
  6. Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. Online e-2006 (2006), 1081-1086
  7. Y. B. Jun, H. S. Kim, and K. J. Lee, The essence of subtraction algebras, Sci. Math. Jpn. Online e-2006 (2006), 1069-1074
  8. Y. B. Jun, Y. H. Kim, and K. J. Lee, Weak forms of subtraction algebras, Bull. Korean Math. Soc. (submitted) https://doi.org/10.4134/BKMS.2008.45.3.437
  9. Y. B. Jun, Y. H. Kim, and K. A. Oh, Subtraction algebras with additional conditions, Commun. Korean Math. Soc. (submitted). https://doi.org/10.4134/CKMS.2007.22.1.001
  10. Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. Online e-2004 (2004), 397-402
  11. Y. B. Jun and K. H. Kim, Prime and irreducible ideals in subtraction algebras, Ital. J. Pure Appl. Math. (submitted)
  12. Y. B. Jun, X. L. Xin, and E. H. Roh, A class of algebras related to BCI-algebras and semigroups, Soochow J. Math. 24 (1998), no. 4, 309-321
  13. Y. H. Kim and H. S. Kim, Subtraction algebras and BCK-algebras, Math. Bohemica 128 (2003), no. 1, 21-24
  14. B. M. Schein, Difference Semigroups, Comm. Algebra 20 (1992), 2153-2169 https://doi.org/10.1080/00927879208824453
  15. B. Zelinka, Subtraction Semigroups, Math. Bohemica 120 (1995), 445-447

Cited by

  1. THE ESSENCE OF SUBTRACTION ALGEBRAS BASED ON N-STRUCTURES vol.27, pp.1, 2012, https://doi.org/10.4134/CKMS.2012.27.1.015
  2. N-IDEALS OF SUBTRACTION ALGEBRAS vol.25, pp.2, 2010, https://doi.org/10.4134/CKMS.2010.25.2.173
  3. ANSWERS TO LEE AND PARK'S QUESTIONS vol.27, pp.1, 2012, https://doi.org/10.4134/CKMS.2012.27.1.001