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中文摘要：
在Quantale理论中，子Quantale是Quantale的一个重要结构，对子Quantale的研究将有助于进一步了解Quantale的内部结构。本文利用映射的方法给出了平凡Quantale的概念，得到了平凡Quantale的具体刻画，并对有限Quantale的子Quantale的个数进行了讨论。最后证明了势为无限的Quantale有无限多个真子Quantale，只含有一个真子Quantale的Quantale的势为3。
英文摘要：
In quantale theory, the subquantale is an important structure of quantale, understanding subquantales is helpful for deeply learning interior structures of quantale. By means of mapping, the concept of trivial quantale is proposed and characterizations for a quantale to be trivial are obtained. Secondly, the number of subquantales included in a finite quantale is discussed. Finally, it is proved that the number of non-trivial subquantales of an infinite quantale is infinite and the cardinality of quantale with one non-trivial subquantale is three.
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