A note on generators of the endomorphism semigroup of an infinite countable chain
- In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
| Author details: | Ilinka DimitrovaORCiDGND, Vitor H. Fernandes, Jörg KoppitzORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1142/S0219498817500311 |
| ISSN: | 0219-4988 |
| ISSN: | 1793-6829 |
| Title of parent work (English): | Journal of Algebra and its Applications |
| Publisher: | World Scientific |
| Place of publishing: | Singapore |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2016/03/02 |
| Publication year: | 2017 |
| Release date: | 2022/07/01 |
| Tag: | Infinite chain; endomorphism semigroup; generators; relative rank |
| Volume: | 16 |
| Issue: | 2 |
| Number of pages: | 9 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
