论文标题
等距性和相互关系
Equidivisibility and profinite coproduct
论文作者
论文摘要
这项工作的目的是研究Pro-$ \ Mathsf {v} $ semogroups类别中相关性下的等价性的行为，其中$ \ MATHSF {V} $是有限的Semigroups的伪造。引入了探索与双面Karnofsky的关系的关系，引入了KR-COVER和强大的KR-Cover的概念。前者比等距更强，后者提供了具有额外温和条件的，所谓的字母超级癌的表征。此外，在假设$ \ mathsf {v} $下关闭的假设是在双面Karnofsky--rhodes扩展下关闭的，封闭了某些类别的均等pro-$ \ $ \ MATHSF {V} $ semigroups in（有限）（有限）$ \ MATHSF {V} $ - coproduct。
The aim of this work is to investigate the behavior of equidivisibility under coproduct in the category of pro-$\mathsf{V}$ semigroups, where $\mathsf{V}$ is a pseudovariety of finite semigroups. Exploring the relationship with the two-sided Karnofsky--Rhodes expansion, the notions of KR-cover and strong KR-cover for profinite semigroups are introduced. The former is stronger than equidivisibility and the latter provides a characterization of equidivisible profinite semigroups with an extra mild condition, so-called letter super-cancellativity. Furthermore, under the assumption that $\mathsf{V}$ is closed under two-sided Karnofsky--Rhodes expansion, closure of some classes of equidivisible pro-$\mathsf{V}$ semigroups under(finite) $\mathsf{V}$-coproduct is established.
