Ends of semigroups

We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.

Citation

Craik , S , Gray , R , Kilibarda , V , Mitchell , J D & Ruskuc , N 2016 , ' Ends of semigroups ' , Semigroup Forum , vol. 93 , no. 2 , pp. 330-346 . https://doi.org/10.1007/s00233-016-9814-9

Publication

Semigroup Forum

Status

Peer reviewed

DOI

https://doi.org/10.1007/s00233-016-9814-9

ISSN

0037-1912

Type

Journal article

Rights

© The Author(s) 2016. This article is published with open access at Springerlink.com. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/9254