Rings of constants for $k$-derivations in $k[x_1, \ldots, x_n]$

Generators of Rings of Constants of Derivations

The aim of this paper is to summarize some motivations and results concerning generators of rings of constants of derivations, especially in the positive characteristic case. 1. Preliminaries. Let k be a field of characteristic p > 0. Denote by k[X] the polynomial algebra k[x1, . . . , xn] and by k(X) the field of rational functions k(x1, . . . , xn). A k-linear mapping d : k[X] → k[X] is calle...

On Jordan generalized k-derivations of semiprime Γ_N-Rings

on jordan generalized k-derivations of semiprime γ_n-rings

Derivations in semiprime rings and Banach algebras

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...

Rings of constants of the form k[f]

Let k[X] be the algebra of polynomials in n variables over a field k of characteristic zero, and let f ∈ k[X] r k. We present a construction of a derivation d of k[X] whose ring of constants is equal to the integral closure of k[f ] in k[X]. A similar construction for fields of rational functions is also given.