论文标题
免费的基于生成的半群：通过增益图的单词问题和结构
Free idempotent generated semigroups: The word problem and structure via gain graphs
论文作者
论文摘要
在先前对杨，古尔德和本作者的广泛研究的基础上，我们为自由生成的半群落而不是有限的生物生成套件提供了对这个单词问题的群体理论后果的更精确的见解。我们证明，这种单词问题实际上等同于计算自由型型生成的semogroup的最大亚组的某些直接产物亚组的相交问题的问题，从而提供了这些单词问题在与霍森财产和库特交叉构造财产相关的群体理论假设下的确定性。我们还提供了一个任意自由生成的半群的全局半群理论结构的基本草图，包括格林关系的表征和非规范$ \ m rathscr {d} $ class的关键参数。特别是，我们证明所有$ \ mathsf {ig}（\ Mathcal {e}）$的所有Schützenberger都必须用于有限的生物材料集$ \ Mathcal {e} $，是$ \ \ Mathsf {ig Mathcal的最大子组之一。
Building on the previous extensive study of Yang, Gould and the present author, we provide a more precise insight into the group-theoretical ramifications of the word problem for free idempotent generated semigroups over finite biordered sets. We prove that such word problems are in fact equivalent to the problem of computing intersections of cosets of certain subgroups of direct products of maximal subgroups of the free idempotent generated semigroup in question, thus providing decidability of those word problems under group-theoretical assumptions related to the Howson property and the coset intersection property. We also provide a basic sketch of the global semigroup-theoretical structure of an arbitrary free idempotent generated semigroup, including the characterisation of Green's relations and the key parameters of non-regular $\mathscr{D}$-classes. In particular, we prove that all Schützenberger groups of $\mathsf{IG}(\mathcal{E})$ for a finite biordered set $\mathcal{E}$ must be among the divisors of the maximal subgroups of $\mathsf{IG}(\mathcal{E})$.
