Generalized Nowicki conjecture

2019/03/05 by Drensky, Vesselin
#13E15 #13N15 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.01788

Abstract

Let B be an integral domain over a field K of characteristic 0. The derivation δ of B[Y_d]=B[y₁,…,y_d] is elementary if δ(B)=0 and δ(y_i)∈ B, i=1,…,d. Then the elements u_ij=δ(y_i)y_j-δ(y_j)y_i, 1≤ i0, i=1,…,d, was handled by Khoury in the first proof of the Nowicki conjecture given by him in 2004. As a consequence of the proof of Kuroda in 2009 if δ(y_i)=f_i(x_i), for any nonconstant polynomials f_i(x_i), i=1,…,d, then B[Y_d]^δ=K[X_d,Y_d]^δ is generated by X_d and U_d=\u_ij=f_i(x_i)y_j-y_if_j(x_j)| 1≤ i

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