On the cancellation problem for L-algebras

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