2008•Gongcheng shuxue xuebaoRequires access
Counting Problems of Subquantales
Bin Zhao
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Abstract
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.