2025/01/24 by Mishra, Sumit Chandra, Mondal, Dibyendu, Shukla, Pankaj
#12H05 #13N15 #13P05 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.14415
Let k be a field of characteristic zero. Let m and α be positive integers. For n≥ 2, let Rn=k[x1,x2,…,xn] with the k-derivation dn given by dn=(1-x1x2α)∂x1+x1m∂x2+x2∂x3+…+xn-1∂xn. We prove that for integers m≥ 2 and α≥ 1, dn is a simple derivation on Rn and dn(Rn) contains no units. This generalizes a result of D. A. Jordan. We also show that the isotropy group of dn is conjugate to a subgroup of translations.