Research Article
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Year 2021, Volume: 6 Issue: 3, 143 - 153, 31.12.2021
https://doi.org/10.30931/jetas.1028567

Abstract

References

  • [1] Deza, E., Deza, M. M., “Figurate Numbers”, World Scientific Publishing, Singapore, (2012).
  • [2] Sparavigna, A. C., “On a generalized sum of the Mersenne Numbers”, Zenodo. http://doi.org/10.5281/zenodo.1250048, (2018).
  • [3] Sparavigna, A. C., “Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3247003, (2019).
  • [4] Sparavigna, A. C., “Groupoids of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3387054, (2019).
  • [5] Ateş, F., Emin, A., “Some New Results on the Orthodox, Strongly 𝜋𝜋- Inverse and 𝜋𝜋-Regularity of Some Monoids”, Bulletin of The Society of Mathematicians Banja Luka, 11(3) (2021) : 463-472.
  • [6] Ateş, F., “Some new monoid and group constructions under semidirect products”, Ars. Combinatoria, 91 (2009) : 203-218.
  • [7] Emin, A., Ateş, F., “A new monoid construction under crossed products”, Journal of Inequalities and Applications, 244(1) (2013).
  • [8] Howie, J. M., “Fundamentals of Semigroup Theory”, No 12, Clarendon Press, Oxford, (1995).
  • [9] Stover, C., Weisstein, E. W., “Groupoid” Retrieved in January, 30, 2021 from http://mathworld.wolfram.com/Groupoid.html, (2021).
  • [10] The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Inc., http://oeis.org, (2021).

Semigroup Construction on Polygonal Numbers

Year 2021, Volume: 6 Issue: 3, 143 - 153, 31.12.2021
https://doi.org/10.30931/jetas.1028567

Abstract

In this paper, some information about polygonal numbers are given. Also, a general binary operator that includes all polygonal numbers are given and it is investigated whether the algebraic structures defined with the general operator specify a semigroup or not.

References

  • [1] Deza, E., Deza, M. M., “Figurate Numbers”, World Scientific Publishing, Singapore, (2012).
  • [2] Sparavigna, A. C., “On a generalized sum of the Mersenne Numbers”, Zenodo. http://doi.org/10.5281/zenodo.1250048, (2018).
  • [3] Sparavigna, A. C., “Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3247003, (2019).
  • [4] Sparavigna, A. C., “Groupoids of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3387054, (2019).
  • [5] Ateş, F., Emin, A., “Some New Results on the Orthodox, Strongly 𝜋𝜋- Inverse and 𝜋𝜋-Regularity of Some Monoids”, Bulletin of The Society of Mathematicians Banja Luka, 11(3) (2021) : 463-472.
  • [6] Ateş, F., “Some new monoid and group constructions under semidirect products”, Ars. Combinatoria, 91 (2009) : 203-218.
  • [7] Emin, A., Ateş, F., “A new monoid construction under crossed products”, Journal of Inequalities and Applications, 244(1) (2013).
  • [8] Howie, J. M., “Fundamentals of Semigroup Theory”, No 12, Clarendon Press, Oxford, (1995).
  • [9] Stover, C., Weisstein, E. W., “Groupoid” Retrieved in January, 30, 2021 from http://mathworld.wolfram.com/Groupoid.html, (2021).
  • [10] The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Inc., http://oeis.org, (2021).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ahmet Emin 0000-0001-7791-7181

Early Pub Date January 20, 2022
Publication Date December 31, 2021
Published in Issue Year 2021 Volume: 6 Issue: 3

Cite

APA Emin, A. (2021). Semigroup Construction on Polygonal Numbers. Journal of Engineering Technology and Applied Sciences, 6(3), 143-153. https://doi.org/10.30931/jetas.1028567
AMA Emin A. Semigroup Construction on Polygonal Numbers. JETAS. December 2021;6(3):143-153. doi:10.30931/jetas.1028567
Chicago Emin, Ahmet. “Semigroup Construction on Polygonal Numbers”. Journal of Engineering Technology and Applied Sciences 6, no. 3 (December 2021): 143-53. https://doi.org/10.30931/jetas.1028567.
EndNote Emin A (December 1, 2021) Semigroup Construction on Polygonal Numbers. Journal of Engineering Technology and Applied Sciences 6 3 143–153.
IEEE A. Emin, “Semigroup Construction on Polygonal Numbers”, JETAS, vol. 6, no. 3, pp. 143–153, 2021, doi: 10.30931/jetas.1028567.
ISNAD Emin, Ahmet. “Semigroup Construction on Polygonal Numbers”. Journal of Engineering Technology and Applied Sciences 6/3 (December 2021), 143-153. https://doi.org/10.30931/jetas.1028567.
JAMA Emin A. Semigroup Construction on Polygonal Numbers. JETAS. 2021;6:143–153.
MLA Emin, Ahmet. “Semigroup Construction on Polygonal Numbers”. Journal of Engineering Technology and Applied Sciences, vol. 6, no. 3, 2021, pp. 143-5, doi:10.30931/jetas.1028567.
Vancouver Emin A. Semigroup Construction on Polygonal Numbers. JETAS. 2021;6(3):143-5.

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