Angeltveit, Vigleik2015-12-070010-437Xhttp://hdl.handle.net/1885/25299We show that there is an essentially unique S-algebra structure on the Morava K-theory spectrum K(n), while K(n) has uncountably many MU or E(n)-algebra structures. Here E(n) is the K(n)-localized Johnson-Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space of A∞ structures on a spectrum, and use the theory of S-algebra k-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol. 6 (2006), 1785-1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.Keywords: moduli space; Morava K-theory; S-algebraUniqueness of Morava K-theory201110.1112/S0010437X100050262016-02-24