  The altermagnetism can achieve spin-split bands in collinear
symmetry-compensated antiferromagnets. Here, we predict altermagnetic order in
Janus monolayer $\mathrm{Cr_2SO}$ with eliminated inversion symmetry, which can
realize the combination of piezoelectricity and altermagnetism in a
two-dimensional material, namely 2D piezoelectric altermagnetism. It is found
that $\mathrm{Cr_2SO}$ is an altermagnetic semiconductor, and the spin-split
bands of both valence and conduction bands are near the Fermi level. The
$\mathrm{Cr_2SO}$ has large out-of-plane piezoelectricity ($|d_{31}|$$=$0.97
pm/V), which is highly desirable for ultrathin piezoelectric device
application. Due to spin-valley locking, both spin and valley can be polarized
by simply breaking the corresponding crystal symmetry with uniaxial strain. Our
findings provide a platform to integrate spin, piezoelectricity and valley in a
single material, which is useful for multi-functional device applications.
