On the adjoint semigroup of a class of logical algebras

摘要

In this paper, a class of logical algebras were studied. Firstly, the characterization of a general implicative BCK-algebra is given. Following this, we prove that the adjoint semigroup of a general implicative BCK-algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK-algebra with condition(s) is a distributive lattice. Finally, we prove the adjoint semigroup of a bounded implicative BCK-algebra is a Boolean algebra.