Abstract
In 1984, A. Restivo and C. Reutenauer solved the Burnside problem for semigroups. They proved that a finitely generated semigroup is finite if and only if it is periodic and has the permutation property P n for some integer n ≥ 2. This fact drown the attention to semigroups satisfying some permutation properties. The semigroups satisfying the permutation property P 2 are exactly the commutative semigroups. All of semigroups considered in this book are generalized commutative semigroups and most of them have some permutation property. In their examinations the commutative semigroups are appeared in subcases. That is why we deal with them in a separated chapter. The literature of commutative semigroups is very rich, but we present only those results which will be used in the other chapters of this book.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Nagy, A. (2001). Commutative semigroups. In: Special Classes of Semigroups. Advances in Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3316-7_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3316-7_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4853-3
Online ISBN: 978-1-4757-3316-7
eBook Packages: Springer Book Archive