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

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Brumatti P., Veloso M.

Colloquium Mathematicum

2011

tom 123

nr 2

277-283

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Brumatti P.

1 Veloso M.

1 2011

Wyniki wyszukiwania

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