Let 𝒮 be a finite cyclic semigroup written additively. An element e of 𝒮 is said to be idempotent if e + e = e. A sequence T over 𝒮 is called idempotent-sum-free provided that no idempotent of 𝒮 can be represented as a sum of one or more terms from T. We prove that an idempotent-sum-free sequence over 𝒮 of length over approximately a half of the size of 𝒮 is well structured. This result generalizes the Savchev–Chen Structure Theorem for zero-sum-free sequences over finite cyclic groups.

中文翻译：

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有限循环半群上长幂等无和序列的结构

让𝒮是一个加法写成的有限循环半群。一个元素e的𝒮据说是幂等的，如果e + e = e. 一个序列吨超过𝒮叫做幂等无和前提是没有幂等的𝒮可以表示为一个或多个项的总和吨. 我们证明了一个幂等无和序列𝒮长度超过大约一半大小的𝒮结构良好。这个结果推广了有限循环群上零和自由序列的 Savchev-Chen 结构定理。