D-n(A) for a class of polynomial automorphisms and stably tameness

[摘要] In this paper we introduce a set, denoted by D-n(A), for every commutative ring A and every positive integer n. It is shown that the elements of this set can be used to give an explicit description of the class H-n(A) introduced in van den Essen and Hubbers [J. Algebra 187 (1997), 214-226]. We deduce that each polynomial map of the form F=X+H with H is an element of H-n(A) can be written as a finite product of automorphisms of the form exp(D), where each D is a locally nilpotent derivation satisfying D-2(X-i) = 0 for all i. Furthermore we deduce that all such Fs are stably tame. (C) 1997 Academic Press.

[发布日期] 1997-06-01