标题： 可分解嵌入和不可约软移位的周期 显示英文标题

标题： Factorizable embeddings and the period of an irreducible sofic shift

摘要： 在推广MacDonald的一个结果的基础上，我们给出了任意子移位嵌入到通过一个不可约有限型子移位（SFT）的不可约软移位的必要且充分条件。 我们还得到了任意子移位嵌入到通过不可约SFT中的\emph{一些}滑动块编码的不可约软移位的必要且充分条件。 我们在该编码被要求为满射时，即作为因子编码时，以及当它被要求为单射或允许为任意编码时，都进行了这样的研究。 这些结果需要不可约软移位的周期概念以及一个$p$-周期性子移位的概念。 开发了周期的几种等价表述。 显示英文摘要

摘要： Generalizing a result of MacDonald we give necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through a given cover by an irreducible subshift of finite type (SFT). We obtain also necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through \emph{some} sliding block code out of an irreducible SFT. We do that when the code is required to be surjective, and hence a factor code, and when it is required to be injective or is allowed to be arbitrary. These results require concepts of the period of an irreducible sofic shift as well as a concept of a $p$-periodic subshift. Several equivalent formulations of the period are developed.