A note on Nakai's conjecture for the ring $K[X₁,...,Xₙ]/(a₁X₁^{m} + ⋯ + aₙXₙ^{m})$

• Autorzy: Paulo Roberto Brumatti , Marcelo Oliveira Veloso
• Języki publikacji: EN

Abstrakty

EN

Let k be a field of characteristic zero, k[X₁,..., Xₙ] the polynomial ring, and B the ring $k[X₁,..., Xₙ]}/(a₁X₁^{m} + ⋯ + aₘXₙ^{m})$, $0 ≠ a_{i} ∈ k$ for all i and m, n ∈ ℕ with n ≥ 2 and m ≥ 1. Let $Der²_{k}(B)$ be the B-module of all second order k-derivations of B and $der²_{k}(B) = Der¹_{k}(B) + Der¹_{k}(B)Der¹_{k}(B)$ where $Der¹_{k}(B)$ is the B-module of k-derivations of B. If m ≥ 2 we exhibit explicitly a second order derivation $D ∈ Der²_{k}(B)$ such that $D ∉ der²_{k}(B)$ and thus we prove that Nakai's conjecture is true for the k-algebra B.

Kategorie tematyczne

• 13N05: Modules of differentials
• 13N15: Derivations
• 13B10: Morphisms
• 13N10: Rings of differential operators and their modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 123
• Numer: 2
• Strony: 277-283

Daty

wydano

2011

Twórcy

autor

Paulo Roberto Brumatti

• IMECC-UNICAMP, 13083-970, Campinas, SP, Brazil

autor

Marcelo Oliveira Veloso

• CAP-UFSJ, 36420-000, Ouro Branco, MG, Brazil

Identyfikatory

DOI

10.4064/cm123-2-10