Skew Difference Algebras

Chajda, Ivan

  • Received : 2007.04.27
  • Accepted : 2009.10.09
  • Published : 2010.03.31


We modify the definition of difference algebra given by J. Meng to obtain a structure which is a directoid with sectional switching involutions with respect to the given partial order. Moreover, we show that this is a representation of our skew difference algebras because every such directoid can be converted into a skew difference algebra.


difference algebra;skew difference algebra;sectional mapping;sectional switching involution;commutative directoid


  1. Ahn S.S., Lee K.J., Remarks on "Representable difference algebras", Kyungpook Math. J., 46(2006), 433-436.
  2. Chajda I., Emanovsky P., Representable difference algebras, Kyungpook Math. J., 44(2004), 335-342.
  3. Chajda I., Halas R., Kuhr J., Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), 71(2005), 19-33.
  4. Jezek J., Quackenbush R., Directoids: algebraic models of up-directed sets, Algebra Universalis, 27(1990), 49-69.
  5. Meng J., Difference algebras, Selected Papers on BCK- and BCI-algebras, 1(1992), 33-39.
  6. Roh E.H., Kim S.Y., Jun Y.B., Shim W.H., On difference algebras, Kyungpook Math. J., 43(2003), 407-414.