  Motivated by ideas from stable homotopy theory we study the space of strongly
homotopy associative multiplications on a two-cell chain complex. In the
simplest case this moduli space is isomorphic to the set of orbits of a group
of invertible power series acting on a certain space. The Hochschild cohomology
rings of resulting A-infinity algebras have an interpretation as totally
ramified extensions of discrete valuation rings. All A-infinity algebras are
supposed to be unital and we give a detailed analysis of unital structures
which is of independent interest.
