 
Summary: ISRAEL JOURNAL OF MATHEMATICS 88 (1994), 221232
ON THE SURJECTIVITY OF SOME TRACE MAPS
BY
ELI ALJADEFF
Department o] Mathematics
Teehnion  Israel Institute of Technology
32000 Hat]a, Israel
ABSTRACT
Let K be a commutative ring with a unit element 1. Let F be a finite
group acting on K via a map t: F * Aut(K). For every subgroup H _< F
define trH: K * K H by trH(x) = ~aeH or(x). We prove
THEOREM: trr is surjective onto K F it" and only if trp is surjective onto
K P for every (cyclic) prime order subgroup P ofF.
This is false for certain noncommutative rings K.
0. Introduction
Let K be a commutative ring with a unit element 1 and let F be a finite group
acting on K via a morphism t: F ~ Aut(K). For every subgroup H of F and
x E K define the trace map tru: K ~ K by
trH(x) = ~ a(x).
aEH
