有限循环半群上长幂等和自由序列的结构
Structure of long idempotent-sum free sequences over finite cyclic semigroups
摘要：
设$\mathcal{S}$是可加写的有限循环半群. $\mathcal{S}$的元素$e$称为幂等的，如果$e+e=e$。$\mathcal{S}$上的序列$T$称为{ \sl幂等和自由}，条件是$\mathcal{S}$的幂等元不能表示为来自$T$的一个或多个项的和。证明了$\mathcal{S}$上长度超过$\mathcal{S}$长度一半的幂等和自由序列是良结构的.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。
英文摘要：
Let $\mathcal{S}$ be a finite cyclic semigroup written additively. An element $e$ of $\mathcal{S}$ is said to be idempotent if $e+e=e$. A sequence $T$ over $\mathcal{S}$ is called {\sl idempotent-sum free} provided that no idempotent of $\mathcal{S}$ can be represented as a sum of one or more terms from $T$. We prove that an idempotent-sum free sequence over $\mathcal{S}$ of length over approximately a half of the size of $\mathcal{S}$ is well-structured. This result generalizes the Savchev-Chen Structure Theorem for zero-sum free sequences over finite cyclic groups.
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