  We investigate the structure of renormalization constants within the MS-like
renormalization prescriptions for a version of dimensional regularization in
which the dimensionful regularization parameter $\Lambda$ differs from the
renormalization point $\mu$. Namely, we rewrite the all-loop equations relating
coefficients at higher $\varepsilon$-poles and higher powers of
$\ln\Lambda/\mu$ to the coefficients of the renormalization group functions in
a simple unified form. It is argued that this form follows from the algebraic
structure of the renormalization group.
