We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups, we address and solve several related enumeration problems.

中文翻译：

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拟平凡半群的分类

我们研究由某些等价关系定义的拟平凡半群的分类。还研究了保持给定全序的拟平凡半群的子类。在有限半群的特殊情况下，我们解决并解决了几个相关的枚举问题。