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تسجيل مستخدم جديدStructure of long idempotent-sum free sequences over finite cyclic semigroups
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Guoqing Wang
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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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