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ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS

Year 2023, Volume: 6 Issue: 1, 99 - 104, 31.01.2023

Şehmus Fındık , Nazar Şahin Öğüşlü

https://doi.org/10.33773/jum.1164153

Abstract

Let $D_4$ be the dihedral group of order $8$. In the present study, we give generators of the algebra of $D_4$ invariants in the polynomial algebra with four generators over a field of characteristic zero.

Keywords

Commutative invariant theory rings

References

  • D. Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann., 36, pp. 473-534 (1890).
  • D. Hilbert, Ueber die vollen Invariantensysteme, Math. Ann., 42, pp. 313-373 (1893).
  • D. Hilbert, Mathematische Probleme, G\"ottinger Nachrichten, pp. 253-297 (1900); Arch. Math. u. Phys., 3(1), pp. 44-63 (1901); Translation: Bull. Amer. Math. Soc., 8(10),pp. 437-479 (1902) .
  • J.E. Humpreys, Hilbert’s Fourteenth Problem, Amer. Math. Monthly Vol., 85 (5), pp. 341-353 (1978).
  • M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math., 81, pp. 766-772 (1959).
  • E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 77, pp. 89-92 (1916).
  • B. Sturmfels, Algorithms in invariant theory. Springer Science and Business Media, (2008).

Year 2023, Volume: 6 Issue: 1, 99 - 104, 31.01.2023

Şehmus Fındık , Nazar Şahin Öğüşlü

https://doi.org/10.33773/jum.1164153

Abstract

References

  • D. Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann., 36, pp. 473-534 (1890).
  • D. Hilbert, Ueber die vollen Invariantensysteme, Math. Ann., 42, pp. 313-373 (1893).
  • D. Hilbert, Mathematische Probleme, G\"ottinger Nachrichten, pp. 253-297 (1900); Arch. Math. u. Phys., 3(1), pp. 44-63 (1901); Translation: Bull. Amer. Math. Soc., 8(10),pp. 437-479 (1902) .
  • J.E. Humpreys, Hilbert’s Fourteenth Problem, Amer. Math. Monthly Vol., 85 (5), pp. 341-353 (1978).
  • M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math., 81, pp. 766-772 (1959).
  • E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 77, pp. 89-92 (1916).
  • B. Sturmfels, Algorithms in invariant theory. Springer Science and Business Media, (2008).
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şehmus Fındık 0000-0001-5717-4413

Nazar Şahin Öğüşlü 0000-0001-7407-9178

Publication Date January 31, 2023
Submission Date August 19, 2022
Acceptance Date October 26, 2022
Published in Issue Year 2023 Volume: 6 Issue: 1

Cite

APA Fındık, Ş., & Öğüşlü, N. Ş. (2023). ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS. Journal of Universal Mathematics, 6(1), 99-104. https://doi.org/10.33773/jum.1164153
AMA Fındık Ş, Öğüşlü NŞ. ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS. JUM. January 2023;6(1):99-104. doi:10.33773/jum.1164153
Chicago Fındık, Şehmus, and Nazar Şahin Öğüşlü. “ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS”. Journal of Universal Mathematics 6, no. 1 (January 2023): 99-104. https://doi.org/10.33773/jum.1164153.
EndNote Fındık Ş, Öğüşlü NŞ (January 1, 2023) ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS. Journal of Universal Mathematics 6 1 99–104.
IEEE Ş. Fındık and N. Ş. Öğüşlü, “ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS”, JUM, vol. 6, no. 1, pp. 99–104, 2023, doi: 10.33773/jum.1164153.
ISNAD Fındık, Şehmus - Öğüşlü, Nazar Şahin. “ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS”. Journal of Universal Mathematics 6/1 (January 2023), 99-104. https://doi.org/10.33773/jum.1164153.
JAMA Fındık Ş, Öğüşlü NŞ. ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS. JUM. 2023;6:99–104.
MLA Fındık, Şehmus and Nazar Şahin Öğüşlü. “ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS”. Journal of Universal Mathematics, vol. 6, no. 1, 2023, pp. 99-104, doi:10.33773/jum.1164153.
Vancouver Fındık Ş, Öğüşlü NŞ. ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS. JUM. 2023;6(1):99-104.
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