TY - JOUR T1 - ON $D_4$ INVARIANTS OF POLYNOMIAL ALGEBRAS AU - Fındık, Şehmus AU - Öğüşlü, Nazar Şahin PY - 2023 DA - January Y2 - 2022 DO - 10.33773/jum.1164153 JF - Journal of Universal Mathematics JO - JUM PB - Gökhan ÇUVALCIOĞLU WT - DergiPark SN - 2618-5660 SP - 99 EP - 104 VL - 6 IS - 1 LA - en AB - 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. KW - Commutative KW - invariant theory KW - rings CR - D. Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann., 36, pp. 473-534 (1890). CR - D. Hilbert, Ueber die vollen Invariantensysteme, Math. Ann., 42, pp. 313-373 (1893). CR - 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) . CR - J.E. Humpreys, Hilbert’s Fourteenth Problem, Amer. Math. Monthly Vol., 85 (5), pp. 341-353 (1978). CR - M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math., 81, pp. 766-772 (1959). CR - E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 77, pp. 89-92 (1916). CR - B. Sturmfels, Algorithms in invariant theory. Springer Science and Business Media, (2008). UR - https://doi.org/10.33773/jum.1164153 L1 - https://dergipark.org.tr/tr/download/article-file/2604852 ER -