DOI QR코드

DOI QR Code

ON IDEALS, FILTERS AND CONGRUENCES IN INCLINES

Yao, Wei;Han, Song-Chol

  • 발행 : 2009.05.31

초록

This paper studies the relations between ideals, filters, regular congruences and normal congruences in inclines. It is shown that for any incline, there are a one-to-one correspondence between all ideals and all regular congruences and a one-to-one correspondence between all filters and all normal congruences.

키워드

incline;ideal;filter;regular congruence;normal congruence

참고문헌

  1. S. S. Ahn and H. S. Kim, On r-ideals in incline algebras, Commun. Korean Math. Soc. 17 (2002), no. 2, 229–235 https://doi.org/10.4134/CKMS.2002.17.2.229
  2. B. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, Mo., 1974
  3. S. C. Han, A Study on Incline Matrices with Indices, Ph.D. Dissertation, Beijing Normal University, China, 2005
  4. Y. B. Jun, S. S. Ahn, and H. S. Kim, Fuzzy subinclines (ideals) of incline algebras, Fuzzy Sets and Systems 123 (2001), no. 2, 217–225 https://doi.org/10.1016/S0165-0114(00)00046-4
  5. K. H. Kim and F. W. Roush, Inclines and incline matrices: a survey, Linear Algebra Appl. 379 (2004), 457–473 https://doi.org/10.1016/j.laa.2003.09.009
  6. K. H. Kim, F. W. Roush, and G. Markowsky, Representation of inclines, Algebra Colloq. 4 (1997), no. 4, 461–470
  7. E. Turunen, Mathematics Behind Fuzzy Logic, Physica-Verlag, Heidelberg, 1999
  8. S. S. Ahn, Y. B. Jun, and H. S. Kim, Ideals and quotients of incline algebras, Commun. Korean Math. Soc. 16 (2001), no. 4, 573–583
  9. Z. Q. Cao, K. H. Kim, and F. W. Roush, Incline Algebra and Applications, John Wiley & Sons, New York, 1984
  10. K. H. Kim and F. W. Roush, Inclines of algebraic structures, Fuzzy Sets and Systems 72 (1995), no. 2, 189–196 https://doi.org/10.1016/0165-0114(94)00350-G

피인용 문헌

  1. ON RIGHT f-DERIVATIONS OF INCLINE ALGEBRAS vol.36, pp.4, 2014, https://doi.org/10.4134/BKMS.2009.46.3.591
  2. SYMMETRIC BI-f-MULTIPLIERS OF INCLINE ALGEBRAS vol.29, pp.3, 2016, https://doi.org/10.4134/BKMS.2009.46.3.591
  3. ON (f, g)-DERIVATIONS OF INCLINE ALGEBRAS vol.27, pp.4, 2014, https://doi.org/10.4134/BKMS.2009.46.3.591
  4. ON RIGHT DERIVATIONS OF INCLINE ALGEBRAS vol.26, pp.4, 2013, https://doi.org/10.4134/BKMS.2009.46.3.591