Archive
2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1




Volume 6, Issue 6, December 2017, Page: 160-163
Some Finiteness Conditions for Strong Semilattice of Semigroups
Basri Çalişkan, Department of Mathematics, Faculty of Arts and Science, Osmaniye Korkut Ata University, Osmaniye, Turkey
Received: Oct. 13, 2017;       Accepted: Oct. 31, 2017;       Published: Dec. 18, 2017
DOI: 10.11648/j.pamj.20170606.12      View  2429      Downloads  120
Abstract
Let be a strong semilattice of semigroups such that is finite and each be a family of disjoint semigroups. In this article some finiteness conditions which are periodicity, local finiteness and locally finite presentability are considered for . It is proven that a strong semilattice of semigroups is periodic, locally finite, locally finitely presented and residually finite, respectively if and only if is finite and each semigroup is periodic, locally finite, locally finitely presented and residually finite, respectively.
Keywords
Strong Semilattice of Semigroups, Finiteness Conditions, Periodicity, Local Finiteness, Locally Finite Presentability, Residual Finiteness
To cite this article
Basri Çalişkan, Some Finiteness Conditions for Strong Semilattice of Semigroups, Pure and Applied Mathematics Journal. Vol. 6, No. 6, 2017, pp. 160-163. doi: 10.11648/j.pamj.20170606.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
N. Ruskuc, “On large subsemigroups and finiteness conditions of semigroups,” Proc. London Math. Soc., vol. 76, 1998, pp. 383-405.
[2]
H. Ayık, N. Ruskuc, “Generators and relations of Rees matrix semigroups,” Proc. Edinburgh Math. Soc., vol. 42, 1999, pp. 481-495.
[3]
I. M. Araujo, M. J. J. Branco, V. H. Fernandes, G. M. S. Gomes, N. Ruskuc, “On generators and relations of unions of semigroups,” Semigroup Forum, vol. 63, 2001, pp. 49-62.
[4]
G. Ayık, H. Ayık, Y. Ünlü, “Presentations and word problem for strong semilattices of semigroups,” Algebra and Discrete Mathematics, vol. 4, 2005, pp. 1-8.
[5]
H. Ayık, “On finiteness conditions for Rees matrix semigroups,” Czechoslovak Math. J., vol. 55, 2005, pp. 455-463.
[6]
B. Çalışkan, “On finitness conditions for S, ρ and S/ ρ,” International Journal of Pure and Applied Mathematics, vol. 65 (1), 2010, pp. 1-9.
[7]
R. Gray, N. Ruskuc, “On residual finiteness of monoids, their Schützenberger groups and associated actions”, J. Algebra 407 (2014), 21-45. DOI:10.1016/j.jalgebra.2014.02.025 arXiv:1003.3176.
[8]
I. Dolinka, R. Gray, N. Ruskuc, On regularity and the word problem for free idempotent generated semigroups, Proc. London Math. Soc. 114 (2017), 401-432. DOI: 10.1112/plms.12011arXiv:1412.5167.
[9]
A. Malheiro, “Finite derivation type for semilattices of semigroups,” Semigroup Forum, vol. 84, 2012, pp. 515-526.
[10]
J. M. Howie, “Fundamentals of semigroup theory,” Clarendon Press, Oxford, 358.
Browse journals by subject