LAUSR

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 = ( x 1 , x 2 , … , x n ) 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.