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Deductive systems of BCK-algebras

Sergio A. Celani (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator F * of a deductive system F is the the pseudocomplement of F . These results are more general than that the similar results given by M. Kondo in [7].

Dual commutative hyper K-ideals of type 1 in hyper K-algebras of order 3.

L. Torkzadeh, M. M. Zahedi (2006)

Mathware and Soft Computing

In this note we classify the bounded hyper K-algebras of order 3, which have D1 = {1}, D2 = {1,2} and D3 = {0,1} as a dual commutative hyper K-ideal of type 1. In this regard we show that there are such non-isomorphic bounded hyper K-algebras.

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