On images of locally finite derivations and [formula omitted]-derivations

Abstract

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k(x) of the polynomial algebra k[x], the formal power series algebra k[[x]] and the Laurent formal power series algebra k[[x]][x−1], where x=(x1,x2,…,xn) denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.