  We give natural descriptions of the homology and cohomology algebras of
regular quotient ring spectra of even E-infinity ring spectra. We show that the
homology is a Clifford algebra with respect to a certain bilinear form
naturally associated to the quotient ring spectrum F. To identify the
cohomology algebra, we first determine the derivations of F and then prove that
the cohomology is isomorphic to the exterior algebra on the module of
derivations. We treat the example of the Morava K-theories in detail.
