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Monogenic semigroups. Consider the case of a [monogenic semigroup](monogenic semigroup), that is, a semigroup $S$ generated by a single element $s$. If $S$ is finite, then it can be totally ordered if and only if it is aperiodic, that is, if there exists a positive integer n such that $s^n = s^{n + 1}$. In this case, the order could be $s \leqslant s^2 \...


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