双循环逆半群中的避免集
Avoidable Sets in The Bicyclic Inverse Semigroup
摘要：
如果$S$可以被划分为两个子集$A$和$B$，使得$U$的任何元素都不能被写为$A$的两个不同元素的乘积或$B$的两个不同元素的乘积，则具有二元运算的集合$S$的子集$U$被称为{ \it可避免}。对双循环逆半群的可避免集进行了分类。
英文摘要：
A subset $U$ of a set $S$ with a binary operation is called {\it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of two distinct elements of $B$. The avoidable sets of the bicyclic inverse semigroup are classified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
