Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 112 (2004) 

Tauvel's height formula in iterated differential operator ringsThomas Guédénon152 boulevard du Général Jacques, 1050 Bruxelles, Belgique; email: guedenon@caramail.comAbstract: Let $k$ be a field of positive characteristic, $R$ an associative algebra over $k$ and let $\Delta_{1, n}=\{\delta_1, \ldots, \delta_n\}$ be a finite set of $k$linear derivations from $R$ to $R$. Let $A=R_n=R[\theta _1, \delta_1]\cdots[\theta _n,\delta_n]$ be an iterated differential operator $k$algebra over $R$ such that $\delta_j(\theta_i)\in R_{i1}\theta_i+R_{i1}; 1\leq i<j\leq n$. As central result we show that if $R$ is noetherian affine $\Delta_{1, n}$hypernormal and if Tauvel's height formula holds for the $\Delta_{1, n}$prime ideals of $R$, then Tauvel's height formula holds in $A$. In particular, let $g$ be a completely solvable finitedimensional $k$Lie algebra acting by derivations on $R$ and let $U(g)$ be the enveloping algebra of $g$. If $R$ is noetherian affine $g$hypernormal and if Tauvel's height formula holds for the $g$prime ideals of $R$, then Tauvel's height formula holds in the crossed product of $R$ by $U(g)$. Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
