On the cancellation problem for L-algebras

In this paper, we consider the cancellation problem for the cartesian product of L-algebras. Firstly, we show that L-algebras with prime element 0 and L-algebras satisfying the condition (C) are cancellable. Furthermore, we also prove that the wedge-sum of cancellable L-algebras is cancellable and each L-algebra can be embedded into a cancellable L-algebra. Finally, we give a class of L-algebras satisfying the cancellation law which is different from the above L-algebras.