Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WEAK FORMS OF SUBTRACTION ALGEBRAS

  • Lee, Kyoung-Ja (DEPARTMENT OF MATHEMATICS EDUCATION HANNAM UNIVERSITY) ;
  • Jun, Young-Bae (DEPARTMENT OF MATHEMATICS EDUCATION(AND RINS) GYEONGSANG NATIONAL UNIVERSITY) ;
  • Kim, Young-Hee (DEPARTMENT OF MATHEMATICS CHUNGBUK NATIONAL UNIVERSITY)
  • Published : 2008.08.31
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Abstract

As a weak form of a subtraction algebra, the notion of weak subtraction algebras is introduced, and its examples are given. A method to make a weak subtraction algebra from a quasi-ordered set is provided.

Keywords

References

  1. J. C. Abbott, Sets, Lattices, and Boolean Algebras, Allyn and Bacon, Inc., Boston, Mass. 1969
  2. G. Birkhoff, Lattice Theory, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV American Mathematical Society, Providence, R.I. 1967
  3. Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. 65 (2007), no. 1, 129-134
  4. Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. 61 (2005), no. 3, 459-464
  5. Y. B. Jun and K. H. Kim, Prime and irreducible ideals in subtraction algebras, Ital. J. Pure Appl. Math. (submitted)
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  7. B. Zelinka, Subtraction semigroups, Math. Bohem. 120 (1995), no. 4, 445-447

Cited by

  1. SOFT WS-ALGEBRAS vol.23, pp.3, 2008, https://doi.org/10.4134/CKMS.2008.23.3.313
  2. ORDER SYSTEMS, IDEALS AND RIGHT FIXED MAPS OF SUBTRACTION ALGEBRAS vol.23, pp.1, 2008, https://doi.org/10.4134/CKMS.2008.23.1.001
  3. ANSWERS TO LEE AND PARK'S QUESTIONS vol.27, pp.1, 2012, https://doi.org/10.4134/CKMS.2012.27.1.001