论文标题
有限循环半群上长期自由和自由序列的结构
Structure of long idempotent-sum free sequences over finite cyclic semigroups
论文作者
论文摘要
令$ \ Mathcal {S} $成为有限的环状半群，上面写着。如果$ e+e = e $，则$ \ mathcal {s} $的元素$ e $ of Mathcal {s} $。如果没有$ \ Mathcal {s} $不可用表示为$ t $的一个或多个项的总和，则$ \ MATHCAL {s} $上的序列$ t $称为{\ sl idempotent-sum free}。我们证明，在$ \ Mathcal {s} $的大约一半的一半上，一个长度的$ \ mathcal {s} $上的iDempotent-sum和序列是结构良好的。该结果概括了有限循环组的零和无序列的Savchev-Chen结构定理。
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.
