Some Finiteness Conditions for Strong Semilattice of Semigroups
Pure and Applied Mathematics Journal
Volume 6, Issue 6, December 2017, Pages: 160-163
Received: Oct. 13, 2017; Accepted: Oct. 31, 2017; Published: Dec. 18, 2017
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Author
Basri Çalişkan, Department of Mathematics, Faculty of Arts and Science, Osmaniye Korkut Ata University, Osmaniye, Turkey
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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.
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