  Decoherence of quantum systems is described by quantum channels. However, a
complete understanding of such channels, especially in the multi-particle
setting, is still an ongoing difficult task. We propose the family of quantum
maps that preserve or completely erase the components of a multi-qubit system
in the basis of Pauli strings, which we call Pauli component erasing maps. For
the corresponding channels, it is shown that the preserved components can be
interpreted as a finite vector subspace, from which we derive several
properties and complete the characterization. Moreover, we show that the
obtained family of channels forms a semigroup and derive its generators. We use
this simple structure to determine physical implementations and connect the
obtained family of channels with Markovian processes.
