  We study the superconducting instability in disordered non-centrosymmetric
monolayers with intrinsic Ising spin-orbit coupling (SOC) subjected to an
in-plane Zeeman magnetic field. The pairing interaction contains the channels
allowed by crystal symmetry, such that in general, the pairing state is a
mixture of singlet and triplet Cooper pairs. The joint action of SOC and Zeeman
field selects a specific in-plane $\mathbf{d}$-vector triplet component to
couple with the singlets, which gains robustness against disorder through the
coupling. The out-of-plane $\mathbf{d}$-vector component, that in the clean
case is immune to both the Zeeman field and SOC is obliterated by a very small
impurity scattering rate. We formulate the quasi-classical theory of Ising
superconductors and solve the linearized Eilenberger equations to obtain the
pair-breaking equations that determine the Zeeman field -- temperature
dependence of the continuous superconducting transition. Our discussion
emphasizes how the Zeeman field, SOC and disorder affect the different
superconducting order parameters, and we show how the spin-fields inevitably
induce odd-frequency pairing correlations.
