  This study proposes \emph{modular arithmetic erasure channels} (MAECs), a
novel class of erasure-like channels with an input alphabet that need not be
binary. This class contains the binary erasure channel (BEC) and some other
known erasure-like channels as special cases. For MAECs, we provide recursive
formulas of Ar{\i}kan-like polar transform to simulate channel polarization. In
other words, we show that the synthetic channels of MAECs are equivalent to
other MAECs. This is a generalization of well-known recursive formulas of the
polar transform for BECs. Using our recursive formulas, we also show that a
recursive application of the polar transform for MAECs results in
\emph{multilevel channel polarization,} which is an asymptotic phenomenon that
is characteristic of non-binary polar codes. Specifically, we establish a
method to calculate the limiting proportions of the partially noiseless and
noisy channels that are generated as a result of multilevel channel
polarization for MAECs. In the particular case of MAECs, this calculation
method solves an open problem posed by Nasser (2017) in the study of non-binary
polar codes.
