Artículos de revistas
A Note On Nakai's Conjecture For The Ring K[x 1... X N]/(a 1x M 1+... + A Nx M N)
Registro en:
Colloquium Mathematicum. , v. 123, n. 2, p. 277 - 283, 2011.
101354
10.4064/cm123-2-10
2-s2.0-84858830473
Autor
Brumatti P.R.
Veloso M.O.
Institución
Resumen
Let k be a field of characteristic zero, K[X 1... X n]=(a 1X m 1+... + a nX m n), 0 ≠ a i Ie{cyrillic, ukrainian} k for all i and m; n Ie{cyrillic, ukrainian} ℕ with n ≥ 2 and m ≥ 1. Let Der 2 k(B) be the B-module of all second order k-derivations of B and der 2 k(B) = Der 1 k(B) + Der 1 k(B) Der 1 k(B) where Der 1 k(B) is the B-module of k-derivations of B. If m ≥ 2 we exhibit explicitly a second order derivation D Ie{cyrillic, ukrainian} Der 2 k(B) such that D = ∉ der 2 k(B) and thus we prove that Nakai's conjecture is true for the k-algebra B. © Instytut Matematyczny PAN, 2011. 123 2 277 283 Grothendieck, A., (1967) Éléments de Géométrie Algébrique, , Publ. Math. IHES 32 Lipman, J., Free derivation modules on algebraic varieties (1965) Amer. J. Math., 87, pp. 874-898 Nakai, Y., High order derivations I (1970) Osaka J. Math., 7, pp. 1-27 Schreiner, A., On a conjecture of Nakai (1994) Arch. Math. (Basel), 62, pp. 506-512 Singh, B., Diérential operators on a hypersurface (1986) Nagoya Math. J., 103, pp. 67-84