Document Zbl 0859.06016

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Adjoint semigroups of BCI-algebras. (English) Zbl 0859.06016

Southeast Asian Bull. Math. 19, No. 3, 95-98 (1995).

Summary: The notion of adjoint semigroups of BCI-algebras is introduced. We prove that there is a bijection between the ideals of a BCK-algebra \(X\) and the filters of the order-adjoint semigroup \(M(X)\). Moreover, positive implicative BCK-algebras will be characterized by their adjoint semigroups.

Cited in 2 Reviews

Cited in 2 Documents

MSC:

06F35

BCK-algebras, BCI-algebras

Keywords:

adjoint semigroups; BCI-algebras; ideals; filters; positive implicative

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