In this paper we study the cancellation law for the tensor product in the category \(\mathsf {Sup}\) of complete lattices and join-preserving maps. First, we investigate the tensor product of generalized power-set lattices. Based on which, we prove that the cancellation law for the tensor product has a close relation to that for the cartesian product of posets, and give a class of complete lattices which do not satisfy the cancellation law for the tensor product. Then, we also investigate the cancellation law for particular subclasses of complete lattices.

中文翻译：

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完全格张量积对消律的一些部分结果

在本文中，我们研究了完全格和保留连接映射的类别\(\mathsf {Sup}\)中张量积的抵消律。首先，我们研究广义幂集格的张量积。在此基础上，我们证明了张量积的抵消律与偏集的笛卡尔积的抵消律有密切的关系，并给出了一类不满足张量积抵消律的完全格。然后，我们还研究了完全格的特定子类的抵消律。