Inverse subsemigroups of finite index in finitely generated inverse semigroups

被引：0

作者：

Amal AlAli

N. D. Gilbert

机构：

[1] Princess Nourah bint Abdulrahman University,Mathematics Department

[2] Heriot-Watt University,School of Mathematical and Computer Sciences, Maxwell Institute for the Mathematical Sciences

来源：

Semigroup Forum | 2018年 / 96卷

关键词：

Inverse semigroup; Coset; Index;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study some aspects of Schein’s theory of cosets for closed inverse subsemigroups of inverse semigroups. We establish an index formula for chains of subsemigroups, and an analogue of M. Hall’s Theorem on the number of cosets of a fixed finite index. We then investigate the relationships between the following properties of a closed inverse submonoid of an inverse monoid: having finite index; being a recognizable subset; being a rational subset; being finitely generated (as a closed inverse submonoid). A remarkable result of Margolis and Meakin shows that these properties are equivalent for a closed inverse submonoid of a free inverse monoid.

引用

页码：489 / 505

页数：16

共 14 条

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