Is every Adams ring morphism a lambda-ring morphism?

A lambda-ring $R$ is called "special" if it satisfies the $lambda^ileft(xyright)=...$ and $lambda^ileft(lambda^jleft(xright)right)=...$ relations, or, equivalently, if the map $lambda_T:RtoLambdaleft(Rright)$ given by $lambda_Tleft(xright)=sumlimits_{i=0}^{infty}lambda^ileft(xright)T^i$ (where the $sum$ sign means addition in $Rleft[left[Tright]right]$, not addition in $Lambdaleft(Rright)$) is a morphism of lambda-rings. If you are wondering what the hell I am talking about, most likely you belong to the school of algebraists that denote only special lambda-rings as lambda-rings at all.

Anyway, let $A$ and $B$ be two special lambda-rings, and for every $i>0$, let $Psi_A^i$ and $Psi_B^i$ be the $i$-th Adams operations on $A$ and $B$, respectively. Let $f:Ato B$ be a ring homomorphism such that $fcircPsi_A^i=Psi_B^icirc f$ for every $i>0$. Does this yield that $f$ is a lambda-ring homomorphism, i. e. that $fcirclambda_A^i=lambda_B^icirc f$ for every $i>0$ ?

Note that this is clear if both $A$ and $B$ are torsion-free as additive groups (i. e., none of the elements $1$, $2$, $3$, ... is a zero-divisor in any of the rings $A$ and $B$), but Hazewinkel, in his text Witt vectors, part 1 (Lemma 16.35), claims the same result for the general case. I am writing a list of errata for his text, and I would like to know whether this should be included - well, and I'd like to know the answer anyway, as I am writing some notes on lambda-rings as well.

For the sake of completeness, here is a definition of Adams operations: These are the maps $Psi^i:Rto R$ for every integer $i>0$ (where $R$ is a special lambda-ring) defined by the equation

$sumlimits_{i=1}^{infty} Psi^ileft(xright)T^i = -Tfrac{d}{dT}logleft(lambda_{-T}left(xright)right)$ in the ring $Rleft[left[Tright]right]$ for every $xin R$.

Here, even if the term $logleft(lambda_{-T}left(xright)right)$ may not make sense (since some of the fractions $frac{1}{1}$, $frac{1}{2}$, $frac{1}{3}$, ... may not exist in $R$), the logarithmic derivative $frac{d}{dT}logleft(lambda_{-T}left(xright)right)$ is defined formally by

$displaystyle frac{d}{dT}logleft(lambda_{-T}left(xright)right)=frac{frac{d}{dT}lambda_{-T}left(xright)}{lambda_{-T}left(xright)}$.