Research Article

ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS

Volume: 6 Number: 1 January 31, 2023
EN

ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS

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

References

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  2. D. Hilbert, Ueber die vollen Invariantensysteme, Math. Ann., 42, pp. 313-373 (1893).
  3. 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) .
  4. J.E. Humpreys, Hilbert’s Fourteenth Problem, Amer. Math. Monthly Vol., 85 (5), pp. 341-353 (1978).
  5. M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math., 81, pp. 766-772 (1959).
  6. E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 77, pp. 89-92 (1916).
  7. B. Sturmfels, Algorithms in invariant theory. Springer Science and Business Media, (2008).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

January 31, 2023

Submission Date

August 19, 2022

Acceptance Date

October 26, 2022

Published in Issue

Year 2023 Volume: 6 Number: 1

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