Some Finiteness Conditions for Strong Semilattice of Semigroups

Basri Çalişkan

doi:doi:10.11648/j.pamj.20170606.12

| Peer-Reviewed

Some Finiteness Conditions for Strong Semilattice of Semigroups

Basri Çalişkan

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 6)

Received: 13 October 2017 Accepted: 31 October 2017 Published: 18 December 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 6)
DOI	10.11648/j.pamj.20170606.12
Page(s)	160-163
Creative Commons	This is an Open Access article, 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 or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Strong Semilattice of Semigroups, Finiteness Conditions, Periodicity, Local Finiteness, Locally Finite Presentability, Residual Finiteness

References

[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.

Cite This Article

Plain Text BibTeX RIS

APA Style

Basri Çalişkan. (2017). Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure and Applied Mathematics Journal, 6(6), 160-163. https://doi.org/10.11648/j.pamj.20170606.12

Copy | Download

ACS Style

Basri Çalişkan. Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure Appl. Math. J. 2017, 6(6), 160-163. doi: 10.11648/j.pamj.20170606.12

Copy | Download

AMA Style

Basri Çalişkan. Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure Appl Math J. 2017;6(6):160-163. doi: 10.11648/j.pamj.20170606.12

Copy | Download

@article{10.11648/j.pamj.20170606.12,
  author = {Basri Çalişkan},
  title = {Some Finiteness Conditions for Strong Semilattice of Semigroups},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {6},
  pages = {160-163},
  doi = {10.11648/j.pamj.20170606.12},
  url = {https://doi.org/10.11648/j.pamj.20170606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170606.12},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Some Finiteness Conditions for Strong Semilattice of Semigroups
AU  - Basri Çalişkan
Y1  - 2017/12/18
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170606.12
DO  - 10.11648/j.pamj.20170606.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 160
EP  - 163
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170606.12
AB  - 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.
VL  - 6
IS  - 6
ER  -

Copy | Download

Author Information

Basri Çalişkan

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Basri Çalişkan. (2017). Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure and Applied Mathematics Journal, 6(6), 160-163. https://doi.org/10.11648/j.pamj.20170606.12

Copy | Download

ACS Style

Basri Çalişkan. Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure Appl. Math. J. 2017, 6(6), 160-163. doi: 10.11648/j.pamj.20170606.12

Copy | Download

AMA Style

Basri Çalişkan. Some Finiteness Conditions for Strong Semilattice of Semigroups. Pure Appl Math J. 2017;6(6):160-163. doi: 10.11648/j.pamj.20170606.12

Copy | Download

@article{10.11648/j.pamj.20170606.12,
  author = {Basri Çalişkan},
  title = {Some Finiteness Conditions for Strong Semilattice of Semigroups},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {6},
  pages = {160-163},
  doi = {10.11648/j.pamj.20170606.12},
  url = {https://doi.org/10.11648/j.pamj.20170606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170606.12},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Some Finiteness Conditions for Strong Semilattice of Semigroups
AU  - Basri Çalişkan
Y1  - 2017/12/18
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170606.12
DO  - 10.11648/j.pamj.20170606.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 160
EP  - 163
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170606.12
AB  - 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.
VL  - 6
IS  - 6
ER  -

Copy | Download