Infinitesimal thickenings of Morava K-theories

A. Baker has constructed certain sequences of cohomology theories which interpolate between the Johnson–Wilson and the Morava K-theories. We realize the representing sequences of spectra as sequences of MU-algebras. Starting with the fact that the spectra representing the Johnson–Wilson and the Morava K-theories admit such structures, we construct the sequences by inductively forming singular extensions. Our methods apply to other pairs of MU-algebras as well.