MATHEMATICA BOHEMICA, Vol. 128, No. 1, pp. 21-24 (2003)

Subtraction algebras and $BCK$-algebras

Young Hee Kim, Hee Sik Kim

Young Hee Kim, Department of Mathematics, Chungbuk National University, Chongju 361-763, Korea, e-mail:; Hee Sik Kim, Department of Mathematics, Hanyang University, Seoul 133-791, Korea, e-mail:

Abstract: In this note we show that a subtraction algebra is equivalent to an implicative $BCK$-algebra, and a subtraction semigroup is a special case of a $BCI$-semigroup.

Keywords: subtraction algebra, subtraction semigroup, implicative $BCK$-algebra, $BCI$-semigroup

Classification (MSC2000): 06F35

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